gdz.top
Номер 1, страница 167 - гдз по алгебре 8 класс учебник Колягин, Ткачева
Авторы: Колягин Ю. М., Ткачева М. В., Федорова Н. Е., Шабунин М. И.
Тип: Учебник
Издательство: Просвещение
Год издания: 2023 - 2026
Уровень обучения: базовый
Цвет обложки: розовый, голубой
Популярные ГДЗ в 8 классе
Глава 4. Квадратные корни. Параграф 24. Квадратный корень из произведения. Вводные упражнения - номер 1, страница 167.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 207018 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/vy-24-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 206232 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квадратные корни" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "146" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1083 #items: array:1 [ 0 => App\Models\Book {#1049 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 1399 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #original: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:4 [ 0 => App\Models\Term {#1057 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4640 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Колягин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Михайлович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4640 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Колягин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Михайлович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5935 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ткачева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Мария" "field_patronymic" => "Владимировна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5935 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ткачева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Мария" "field_patronymic" => "Владимировна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1059 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 6024 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Федорова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Надежда" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 6024 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Федорова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Надежда" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1060 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 6266 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Шабунин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Михаил" "field_patronymic" => "Иванович" "field_surname_rp" => null ] #original: array:12 [ "id" => 6266 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Шабунин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Михаил" "field_patronymic" => "Иванович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\Term {#1071 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ …6] "field_translit" => "bazovyy" ] #original: array:6 [ "id" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ …6] "field_translit" => "bazovyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1290" "field_priority" => "10" "field_default_folder" => "/algebra_08/kolyagin-u23/" "field_isbn" => null "field_cover" => array:1 [ 0 => "/media/algebra_08/kolyagin-u23/covers/cover1.webp?ts=1734206325" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_08/kolyagin-u23/covers/cover1.webp?ts=1734206325" "alt" => "" "width" => "1200" "height" => "1576" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/algebra/kolyagin-fgos" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1078 #items: array:2 [ 0 => App\Models\Term {#1079 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 53 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "розовый" "field_cases" => array:6 [ …6] "field_translit" => "rozovyy" ] #original: array:6 [ "id" => 53 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "розовый" "field_cases" => array:6 [ …6] "field_translit" => "rozovyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1080 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 52 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "голубой" "field_cases" => array:6 [ …6] "field_translit" => "goluboy" ] #original: array:6 [ "id" => 52 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "голубой" "field_cases" => array:6 [ …6] "field_translit" => "goluboy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => "<!--Текст в низу страницы--> <p> Есть случаи, когда по каким-либо причинам, ученик не может справиться с домашним заданием по алгебре или недостаточно освоил новую тему. На работу с репетиром решаются не все, да и не у каждого родителя на это есть средства. В таких случаях на помощь приходит <strong>ГДЗ по алгебре 8 класс к учебнику Колягина (Просвещение, 2023 г.)</strong> с задачами и решениями. </p> <h2> Кому помогает сборник ответов? </h2> <p> Решебник полностью повторяет все темы, задачи и примеры, которые представлены в учебнике. Это позволяет намного быстрее и проще найти интересующие восьмиклассника решения. Книга будет полезна для: </p> <ul> <li>учеников, которые по причине олимпиад, соревнований или заболеваний, отсутствуют на уроках;</li> <li>подростков, за время урока не смогли освоить новый материал, поэтому затрудняются с выполнением домашнего задания;</li> <li>выпускников, которые готовятся к сдаче ЕГЭ или ОГЭ и им нужно заполнить пробелы в своих знаниях;</li> <li>учеников, которые не уверены в правильности ответа, и хотят проверить, правильно ли они выполнили упражнение;</li> <li>родителей, желающих проверить то, насколько их ребенок верно решил все задачи и примеры в домашнем задании.</li> </ul> <p> Как ни странно, решебниками, порой, пользуются и учителя при проверке классных или домашних работ, когда нет времени на проверку расчетов или последовательности действий в том или ином задании. Есть случаи, когда педагоги используют их, как пособие, при подготовке к уроку. </p> <h2> Польза готовых решений по учебнику Колягина </h2> <p> Использовать помощник при решении домашних заданий нужно правильно, не злоупотребляя информацией в нем. Работа с пособием должна быть направлена на помощь в учебе, а не систематическое списывание готовых решений с него. Такая методика может привести к тому, что ученик не сможет разобраться в пропущенной теме или заполнить пробелы в знаниях, а это в дальнейшем приведет к еще большим проблемам. В старших классах все темы в алгебре связаны между собой и если будет упущена одна, начнется недопонимание и в других. </p> <p> <strong>«ГДЗ по алгебре 8 класс Учебник Ю.М. Колягин, М.В. Ткачева, С.А. Федорова, М.И. Шабунин (ФГОС)»</strong> представляет вспомогательные и учебные материалы, которые предусмотрены на улучшение знаний ученика в школьной программе. Все больше педагогов и родителей соглашаются с тем, что пособие помогает: </p> <ol> <li>грамотно оформлять решения различных примеров и задач;</li> <li>получить навыки самопроверки и самоконтроля;</li> <li>выполнять домашнюю работу быстрее в условиях, когда время на выполнение решений ограничено;</li> <li>найти решение для сложных задач, при решении которых возникают трудности с поиском правильного решения и его грамотным оформлением;</li> <li>сверить полученный ответ с решебником, чтобы вовремя выявить ошибки, разобраться в них и оформить верный ответ.</li> </ol> <p> Помимо готового решения, к каждому готовому решению дается подробное объяснение, что особенно актуально для тех, кто не разбирается в материале или вообще пропустил урок. Дополнительная информация позволяет ученику углубиться в суть задачи и понять смысл каждого арифметического действия. Такой решебник очень полезен, если школьник неправильно решил задачу и хочет разобраться в допущенной ошибке, чтобы исключить ее повторение в будущем. Для ряда заданий есть несколько вариантов решений с пояснениями к каждому отдельно. Обычно это примеры или задачи, которые требуют нестандартного решения, которые отмечены «звездочкой». Иными словами, все упражнения расписаны максимально подробно, поэтому они будут понятны даже ученику, который по каким-либо отсутствовал на уроке. </p> <p> Пособие полностью соответствует новому стандарту ФГОС, по которому написан учебник. В ряде случаев оно помогает сэкономить время и силы школьника на поиск нужной информации. Использование готовых решений при выполнении домашних работ поможет повысить успеваемость и подтянуть свои знания по предмету. При этом ученику перед использованием ГДЗ рекомендуется повторить, теорию и правила, чтобы понимать о чем идет речь в решениях. </p> <h2> Почему ГДЗ по алгебре 8 класс так полезен? </h2> <p> Это пособие, которому можно доверять. Изначально оно успело зарекомендовать себя в печатном варианте, так как учебник используется в программе восьмиклассников уже давно. Онлайн версия помогает намного быстрее найти ответ с подробным решением намного быстрее. При этом она доступна в любое время, даже если школьник находится далеко от дома. Он может в любое время обратиться за помощью к электронной версии, так как современный гаджет с доступом в интернет есть у каждого ученика. </p> <p> ГДЗ составлен опытными методистами, которые имеют многолетний опыт в преподавании алгебры. Перед публикацией пособие проверено на соответствие учебнику по ФГОС, чтобы исключить некачественный контент. Решебник помог уже нескольким тысячам учеников, педагогов и родителей, что подтверждено многочисленными положительными отзывами. </p>" "breadcrumbs" => array:3 [ "class" => 379 "subject" => 542 "class_subject" => 385 ] ] #original: array:50 [ "id" => 1399 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_country" => Illuminate\Database\Eloquent\Collection {#1064} "field_city" => Illuminate\Database\Eloquent\Collection {#1066} "field_series" => Illuminate\Database\Eloquent\Collection {#1068} "field_umk" => Illuminate\Database\Eloquent\Collection {#1069} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1072} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1074} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1290" "field_priority" => "10" "field_default_folder" => "/algebra_08/kolyagin-u23/" "field_isbn" => null "field_cover" => array:1 [ 0 => "/media/algebra_08/kolyagin-u23/covers/cover1.webp?ts=1734206325" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_08/kolyagin-u23/covers/cover1.webp?ts=1734206325" "alt" => "" "width" => "1200" "height" => "1576" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1075} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1076} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1077} "field_url" => "/8-klass/algebra/kolyagin-fgos" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1078} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => "<!--Текст в низу страницы--> <p> Есть случаи, когда по каким-либо причинам, ученик не может справиться с домашним заданием по алгебре или недостаточно освоил новую тему. На работу с репетиром решаются не все, да и не у каждого родителя на это есть средства. В таких случаях на помощь приходит <strong>ГДЗ по алгебре 8 класс к учебнику Колягина (Просвещение, 2023 г.)</strong> с задачами и решениями. </p> <h2> Кому помогает сборник ответов? </h2> <p> Решебник полностью повторяет все темы, задачи и примеры, которые представлены в учебнике. Это позволяет намного быстрее и проще найти интересующие восьмиклассника решения. Книга будет полезна для: </p> <ul> <li>учеников, которые по причине олимпиад, соревнований или заболеваний, отсутствуют на уроках;</li> <li>подростков, за время урока не смогли освоить новый материал, поэтому затрудняются с выполнением домашнего задания;</li> <li>выпускников, которые готовятся к сдаче ЕГЭ или ОГЭ и им нужно заполнить пробелы в своих знаниях;</li> <li>учеников, которые не уверены в правильности ответа, и хотят проверить, правильно ли они выполнили упражнение;</li> <li>родителей, желающих проверить то, насколько их ребенок верно решил все задачи и примеры в домашнем задании.</li> </ul> <p> Как ни странно, решебниками, порой, пользуются и учителя при проверке классных или домашних работ, когда нет времени на проверку расчетов или последовательности действий в том или ином задании. Есть случаи, когда педагоги используют их, как пособие, при подготовке к уроку. </p> <h2> Польза готовых решений по учебнику Колягина </h2> <p> Использовать помощник при решении домашних заданий нужно правильно, не злоупотребляя информацией в нем. Работа с пособием должна быть направлена на помощь в учебе, а не систематическое списывание готовых решений с него. Такая методика может привести к тому, что ученик не сможет разобраться в пропущенной теме или заполнить пробелы в знаниях, а это в дальнейшем приведет к еще большим проблемам. В старших классах все темы в алгебре связаны между собой и если будет упущена одна, начнется недопонимание и в других. </p> <p> <strong>«ГДЗ по алгебре 8 класс Учебник Ю.М. Колягин, М.В. Ткачева, С.А. Федорова, М.И. Шабунин (ФГОС)»</strong> представляет вспомогательные и учебные материалы, которые предусмотрены на улучшение знаний ученика в школьной программе. Все больше педагогов и родителей соглашаются с тем, что пособие помогает: </p> <ol> <li>грамотно оформлять решения различных примеров и задач;</li> <li>получить навыки самопроверки и самоконтроля;</li> <li>выполнять домашнюю работу быстрее в условиях, когда время на выполнение решений ограничено;</li> <li>найти решение для сложных задач, при решении которых возникают трудности с поиском правильного решения и его грамотным оформлением;</li> <li>сверить полученный ответ с решебником, чтобы вовремя выявить ошибки, разобраться в них и оформить верный ответ.</li> </ol> <p> Помимо готового решения, к каждому готовому решению дается подробное объяснение, что особенно актуально для тех, кто не разбирается в материале или вообще пропустил урок. Дополнительная информация позволяет ученику углубиться в суть задачи и понять смысл каждого арифметического действия. Такой решебник очень полезен, если школьник неправильно решил задачу и хочет разобраться в допущенной ошибке, чтобы исключить ее повторение в будущем. Для ряда заданий есть несколько вариантов решений с пояснениями к каждому отдельно. Обычно это примеры или задачи, которые требуют нестандартного решения, которые отмечены «звездочкой». Иными словами, все упражнения расписаны максимально подробно, поэтому они будут понятны даже ученику, который по каким-либо отсутствовал на уроке. </p> <p> Пособие полностью соответствует новому стандарту ФГОС, по которому написан учебник. В ряде случаев оно помогает сэкономить время и силы школьника на поиск нужной информации. Использование готовых решений при выполнении домашних работ поможет повысить успеваемость и подтянуть свои знания по предмету. При этом ученику перед использованием ГДЗ рекомендуется повторить, теорию и правила, чтобы понимать о чем идет речь в решениях. </p> <h2> Почему ГДЗ по алгебре 8 класс так полезен? </h2> <p> Это пособие, которому можно доверять. Изначально оно успело зарекомендовать себя в печатном варианте, так как учебник используется в программе восьмиклассников уже давно. Онлайн версия помогает намного быстрее найти ответ с подробным решением намного быстрее. При этом она доступна в любое время, даже если школьник находится далеко от дома. Он может в любое время обратиться за помощью к электронной версии, так как современный гаджет с доступом в интернет есть у каждого ученика. </p> <p> ГДЗ составлен опытными методистами, которые имеют многолетний опыт в преподавании алгебры. Перед публикацией пособие проверено на соответствие учебнику по ФГОС, чтобы исключить некачественный контент. 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#primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 206232 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квадратные корни" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "146" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 206232 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квадратные корни" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125} "field_page_start" => "146" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1126} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1128 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 206245 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квадратный корень из произведения" "field_branch_order" => "24" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Term {#1129 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "165" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 206245 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квадратный корень из произведения" "field_branch_order" => "24" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132} "field_page_start" => "165" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1131} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1133 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 206247 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Вводные упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1134 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "167" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1135 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1144 #items: array:1 [ 0 => App\Models\Branch {#1143 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 206245 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квадратный корень из произведения" "field_branch_order" => "24" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1145 …2} "field_page_start" => "165" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1146 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1147 …2} ] #original: array:24 [ "id" => 206245 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квадратный корень из произведения" "field_branch_order" => "24" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1145 …2} "field_page_start" => "165" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1146 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1147 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 206247 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Вводные упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1134} "field_page_start" => "167" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1135} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1144} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:2 [ 0 => App\Models\Element {#1106 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 231190 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Edition {#1105 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 715 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "tolik" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_content_source" => null ] #original: array:21 [ "id" => 715 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "tolik" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "207018" "type" => "task" ] "text" => "<p><strong>1.</strong> Вычислить:</p><p><strong>1)</strong> $5 \cdot \sqrt{49};$</p><p><strong>2)</strong> $-10 \cdot \sqrt{(-10)^2};$</p><p><strong>3)</strong> $-7 \cdot \sqrt{(-2)^4};$</p><p><strong>4)</strong> $\sqrt{3 \cdot 27}.$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1633" "height" => 152 "path" => "/media/algebra_08/kolyagin-u23/0-vy-24/1-1.webp?ts=1734247697" ] ] ] #original: array:7 [ "id" => 231190 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098} "task" => array:2 [ "refs" => "207018" "type" => "task" ] "text" => "<p><strong>1.</strong> Вычислить:</p><p><strong>1)</strong> $5 \cdot \sqrt{49};$</p><p><strong>2)</strong> $-10 \cdot \sqrt{(-10)^2};$</p><p><strong>3)</strong> $-7 \cdot \sqrt{(-2)^4};$</p><p><strong>4)</strong> $\sqrt{3 \cdot 27}.$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1633" "height" => 152 "path" => "/media/algebra_08/kolyagin-u23/0-vy-24/1-1.webp?ts=1734247697" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1099 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1417731 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Edition {#1097 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5309 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4" "field_order" => "5" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5309 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4" "field_order" => "5" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "207018" "type" => "task" ] "text" => "<p><strong>1)</strong> Чтобы вычислить значение выражения $5 \cdot \sqrt{49}$, необходимо найти значение квадратного корня из 49. Арифметический квадратный корень из 49 равен 7, поскольку $7^2 = 49$. После этого умножим 5 на полученное значение.<br>$5 \cdot \sqrt{49} = 5 \cdot 7 = 35$.<br>Ответ: 35</p><p><strong>2)</strong> Для вычисления $-10 \cdot \sqrt{(-10)^2}$ сначала выполним действие под знаком корня. Возведем число -10 в квадрат: $(-10)^2 = 100$. Теперь выражение имеет вид $-10 \cdot \sqrt{100}$. Квадратный корень из 100 равен 10. Далее умножим -10 на 10.<br>$-10 \cdot \sqrt{(-10)^2} = -10 \cdot \sqrt{100} = -10 \cdot 10 = -100$.<br>Также можно применить тождество $\sqrt{a^2} = |a|$, согласно которому $\sqrt{(-10)^2} = |-10| = 10$. Результат будет таким же: $-10 \cdot 10 = -100$.<br>Ответ: -100</p><p><strong>3)</strong> В выражении $-7 \cdot \sqrt{(-2)^4}$ начнем с вычисления подкоренного выражения. Возведем -2 в четвертую степень: $(-2)^4 = (-2) \cdot (-2) \cdot (-2) \cdot (-2) = 16$. Теперь выражение можно записать как $-7 \cdot \sqrt{16}$. Квадратный корень из 16 равен 4. Умножим -7 на 4.<br>$-7 \cdot \sqrt{(-2)^4} = -7 \cdot \sqrt{16} = -7 \cdot 4 = -28$.<br>Ответ: -28</p><p><strong>4)</strong> Чтобы вычислить произведение $\sqrt{3} \cdot \sqrt{27}$, применим свойство корней, которое гласит, что произведение корней равно корню из произведения: $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ для неотрицательных $a$ и $b$.<br>$\sqrt{3} \cdot \sqrt{27} = \sqrt{3 \cdot 27} = \sqrt{81}$.<br>Квадратный корень из 81 равен 9, так как $9^2 = 81$.<br>Ответ: 9</p>" ] #original: array:6 [ "id" => 1417731 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "207018" "type" => "task" ] "text" => "<p><strong>1)</strong> Чтобы вычислить значение выражения $5 \cdot \sqrt{49}$, необходимо найти значение квадратного корня из 49. Арифметический квадратный корень из 49 равен 7, поскольку $7^2 = 49$. После этого умножим 5 на полученное значение.<br>$5 \cdot \sqrt{49} = 5 \cdot 7 = 35$.<br>Ответ: 35</p><p><strong>2)</strong> Для вычисления $-10 \cdot \sqrt{(-10)^2}$ сначала выполним действие под знаком корня. Возведем число -10 в квадрат: $(-10)^2 = 100$. Теперь выражение имеет вид $-10 \cdot \sqrt{100}$. Квадратный корень из 100 равен 10. Далее умножим -10 на 10.<br>$-10 \cdot \sqrt{(-10)^2} = -10 \cdot \sqrt{100} = -10 \cdot 10 = -100$.<br>Также можно применить тождество $\sqrt{a^2} = |a|$, согласно которому $\sqrt{(-10)^2} = |-10| = 10$. Результат будет таким же: $-10 \cdot 10 = -100$.<br>Ответ: -100</p><p><strong>3)</strong> В выражении $-7 \cdot \sqrt{(-2)^4}$ начнем с вычисления подкоренного выражения. Возведем -2 в четвертую степень: $(-2)^4 = (-2) \cdot (-2) \cdot (-2) \cdot (-2) = 16$. Теперь выражение можно записать как $-7 \cdot \sqrt{16}$. Квадратный корень из 16 равен 4. Умножим -7 на 4.<br>$-7 \cdot \sqrt{(-2)^4} = -7 \cdot \sqrt{16} = -7 \cdot 4 = -28$.<br>Ответ: -28</p><p><strong>4)</strong> Чтобы вычислить произведение $\sqrt{3} \cdot \sqrt{27}$, применим свойство корней, которое гласит, что произведение корней равно корню из произведения: $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ для неотрицательных $a$ и $b$.<br>$\sqrt{3} \cdot \sqrt{27} = \sqrt{3 \cdot 27} = \sqrt{81}$.<br>Квадратный корень из 81 равен 9, так как $9^2 = 81$.<br>Ответ: 9</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "207019" "type" => "task" ] "previous" => array:2 [ "refs" => "207017" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\BookPage {#1111 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 929633 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_url" => "/8-klass/algebra/kolyagin-fgos/page-167" "field_display_title" => "167" "field_folder" => "1" "field_image_name" => "167" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Element {#1039 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1104025 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1113 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1104025 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1113 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "929634" "type" => "book_page" ] "previous" => array:2 [ "refs" => "929632" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1208 #items: array:11 [ 0 => App\Models\Task {#1226 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 207013 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/yv-24-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1227 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1228 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1229 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1310 …2} "content" => Illuminate\Database\Eloquent\Collection {#1267 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1300 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 207013 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/yv-24-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1227 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1228 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1229 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1310 …2} "content" => Illuminate\Database\Eloquent\Collection {#1267 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1300 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1303 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 207014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/yv-24-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1317 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1301 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1307 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1304 …2} "content" => Illuminate\Database\Eloquent\Collection {#1308 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1290 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 207014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/yv-24-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1317 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1301 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1307 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1304 …2} "content" => Illuminate\Database\Eloquent\Collection {#1308 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1290 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1295 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 207015 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/yv-24-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1271 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1289 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1293 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1294 …2} "content" => Illuminate\Database\Eloquent\Collection {#1292 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1279 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 207015 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/yv-24-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1271 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1289 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1293 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1294 …2} "content" => Illuminate\Database\Eloquent\Collection {#1292 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1279 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1283 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 207016 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/yv-24-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1291 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1277 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1281 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1278 …2} "content" => Illuminate\Database\Eloquent\Collection {#1282 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1230 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 207016 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/yv-24-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1291 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1277 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1281 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1278 …2} "content" => Illuminate\Database\Eloquent\Collection {#1282 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1230 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1305 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 207017 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/yv-24-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1280 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1233 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1268 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1306 …2} "content" => Illuminate\Database\Eloquent\Collection {#1270 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1257 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 207017 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/yv-24-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1280 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1233 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1268 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1306 …2} "content" => Illuminate\Database\Eloquent\Collection {#1270 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1257 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1262 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 207018 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/vy-24-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1269 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1256 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1259 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1261 …2} "content" => Illuminate\Database\Eloquent\Collection {#1258 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1260 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 207018 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "167" "field_page_end" => null "field_url" => "/8-klass/algebra/kolyagin-fgos/vy-24-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1269 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] …8 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 6 => App\Models\Task {#1249 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 7 => App\Models\Task {#1244 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 8 => App\Models\Task {#1309 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 9 => App\Models\Task {#1337 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 10 => App\Models\Task {#1349 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 929633 "created_at" => "2026-04-10 13:58:26" "updated_at" => 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№1 (с. 167)
Условие. №1 (с. 167)
скриншот условия
1. Вычислить:
1) $5 \cdot \sqrt{49};$
2) $-10 \cdot \sqrt{(-10)^2};$
3) $-7 \cdot \sqrt{(-2)^4};$
4) $\sqrt{3 \cdot 27}.$
Решение 4. №1 (с. 167)
1) Чтобы вычислить значение выражения $5 \cdot \sqrt{49}$, необходимо найти значение квадратного корня из 49. Арифметический квадратный корень из 49 равен 7, поскольку $7^2 = 49$. После этого умножим 5 на полученное значение.
$5 \cdot \sqrt{49} = 5 \cdot 7 = 35$.
Ответ: 35
2) Для вычисления $-10 \cdot \sqrt{(-10)^2}$ сначала выполним действие под знаком корня. Возведем число -10 в квадрат: $(-10)^2 = 100$. Теперь выражение имеет вид $-10 \cdot \sqrt{100}$. Квадратный корень из 100 равен 10. Далее умножим -10 на 10.
$-10 \cdot \sqrt{(-10)^2} = -10 \cdot \sqrt{100} = -10 \cdot 10 = -100$.
Также можно применить тождество $\sqrt{a^2} = |a|$, согласно которому $\sqrt{(-10)^2} = |-10| = 10$. Результат будет таким же: $-10 \cdot 10 = -100$.
Ответ: -100
3) В выражении $-7 \cdot \sqrt{(-2)^4}$ начнем с вычисления подкоренного выражения. Возведем -2 в четвертую степень: $(-2)^4 = (-2) \cdot (-2) \cdot (-2) \cdot (-2) = 16$. Теперь выражение можно записать как $-7 \cdot \sqrt{16}$. Квадратный корень из 16 равен 4. Умножим -7 на 4.
$-7 \cdot \sqrt{(-2)^4} = -7 \cdot \sqrt{16} = -7 \cdot 4 = -28$.
Ответ: -28
4) Чтобы вычислить произведение $\sqrt{3} \cdot \sqrt{27}$, применим свойство корней, которое гласит, что произведение корней равно корню из произведения: $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ для неотрицательных $a$ и $b$.
$\sqrt{3} \cdot \sqrt{27} = \sqrt{3 \cdot 27} = \sqrt{81}$.
Квадратный корень из 81 равен 9, так как $9^2 = 81$.
Ответ: 9
Другие задания:
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