Chers finalistes, préparez-vous pour le grand jour avec nos contenus !

Des items de toutes les options taillés sur mesure pour que vous prépariez mieux vos épreuves

Start learning
FRACTIONS IRRATIONNELLES
Domaine Science Sous domaine Mathématiques
Section Technique Option Hôtellerie et Restauration
Discipline Algèbre Classe 4ème
Matériel didactique Calculatrices Auteur SCHOOLAP.COM
Objectif opérationnel A la fin de la leçon, l'élève sera capable de définir une fraction et de calculer ses termes.
Réference Programme national de math 2005, KAYEMBE et Cie, maîtriser les maths 3 page 92
Activité initiale

Rappel

Effectuer les calcules suivants :

Rappel

Effectuer les calcules suivants :

Motivation

Comment appelle-t-on un terme ayant le numérateur et le dénominateur?

Motivation

Un terme ayant le numérateur et le dénominateur est appelé la fraction.

Annonce du Sujet

Aujourd'hui nous allons étudier les fractions irrationnelles.

Annonce du Sujet

Aujourd'hui nous allons étudier les fractions irrationnelles.

Activité principale

Analyse 

Définir une fraction irrationnelle

Analyse

Définition

Une fraction irrationnelle est celle dont un des termes au moins renferme un signe radical.

Il est recommandé de transformer une fraction dont le dénominateur est irrationnel en une fraction dont le dénominateur est rationnel.

Le dénominateur est un monôme 

Synthèse

Qu'est-ce que nous venons de voir?

Nous venons de voir la fraction irrationnelle.

8.1.28PHP Version238msRequest Duration5MBMemory UsageGET fiches/{id}/{slug}Route
    • Booting (29.22ms)
    • Application (209ms)
    • 1 x Application (87.71%)
      209.05ms
      1 x Booting (12.26%)
      29.22ms
      7 templates were rendered
      • public.fiches.show (resources/views/public/fiches/show.blade.php)2bladefile
        Params
        0
        post
        1
        posts
      • components.banner-page (resources/views/components/banner-page.blade.php)7bladefile
        Params
        0
        property
        1
        firstTitle
        2
        secondTitle
        3
        src
        4
        attributes
        5
        slot
        6
        __laravel_slots
      • components.ad-card-lesson-long (resources/views/components/ad-card-lesson-long.blade.php)7bladefile
        Params
        0
        summary
        1
        title
        2
        actionLink
        3
        actionText
        4
        attributes
        5
        slot
        6
        __laravel_slots
      • components.button-link (resources/views/components/button-link.blade.php)6bladefile
        Params
        0
        class
        1
        title
        2
        href
        3
        attributes
        4
        slot
        5
        __laravel_slots
      • layouts.public (resources/views/layouts/public.blade.php)10bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        posts
        5
        component
        6
        __currentLoopData
        7
        post_
        8
        loop
        9
        content
      • layouts.include.public.header (resources/views/layouts/include/public/header.blade.php)10bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        posts
        5
        component
        6
        __currentLoopData
        7
        post_
        8
        loop
        9
        content
      • layouts.include.public.footer (resources/views/layouts/include/public/footer.blade.php)10bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        posts
        5
        component
        6
        __currentLoopData
        7
        post_
        8
        loop
        9
        content
      uri
      GET fiches/{id}/{slug}
      middleware
      web
      controller
      App\Http\Controllers\Public\FicheController@show
      as
      public.fiche.show
      namespace
      prefix
      /fiches
      where
      file
      app/Http/Controllers/Public/FicheController.php:46-73
      14 statements were executed179ms
      • select * from `oldt_posts` where `oldt_posts`.`id` = '2478' limit 1
        2.53ms/app/Repositories/PostRepository.php:39schoolap
        Metadata
        Bindings
        • 0. 2478
        Backtrace
        • 19. /app/Repositories/PostRepository.php:39
        • 20. /app/Http/Controllers/Public/FicheController.php:48
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `lessons` where (`post_id` = 2478) and `lessons`.`deleted_at` is null limit 1
        1.44ms/app/Http/Controllers/Public/FicheController.php:52schoolap
        Metadata
        Bindings
        • 0. 2478
        Backtrace
        • 15. /app/Http/Controllers/Public/FicheController.php:52
        • 16. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • update `lessons` set `count_view` = `count_view` + 1, `lessons`.`updated_at` = '2025-05-12 04:57:16' where `id` = 2819 and `lessons`.`deleted_at` is null
        2.86ms/app/Http/Controllers/Public/FicheController.php:55schoolap
        Metadata
        Bindings
        • 0. 2025-05-12 04:57:16
        • 1. 2819
        Backtrace
        • 16. /app/Http/Controllers/Public/FicheController.php:55
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `oldt_posts` where `published` = 1 order by RAND() limit 4
        60.14ms/app/Http/Controllers/Public/FicheController.php:61schoolap
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 14. /app/Http/Controllers/Public/FicheController.php:61
        • 15. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 16. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `oldt_material_sheets` where `oldt_material_sheets`.`id` = 2094 limit 1
        1.38msview::public.fiches.show:7schoolap
        Metadata
        Bindings
        • 0. 2094
        Backtrace
        • 20. view::public.fiches.show:7
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `oldt_grades` where `oldt_grades`.`id` = 4 and `oldt_grades`.`id` is not null limit 1
        490μsview::public.fiches.show:15schoolap
        Metadata
        Bindings
        • 0. 4
        Backtrace
        • 20. view::public.fiches.show:15
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `oldt_options` where `oldt_options`.`id` = 27 limit 1
        350μsview::public.fiches.show:15schoolap
        Metadata
        Bindings
        • 0. 27
        Backtrace
        • 20. view::public.fiches.show:15
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `oldt_disciplines` where `oldt_disciplines`.`id` = 1 limit 1
        830μsview::public.fiches.show:15schoolap
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 20. view::public.fiches.show:15
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `oldt_sub_domains` where `oldt_sub_domains`.`id` = 1 and `oldt_sub_domains`.`id` is not null limit 1
        680μsview::public.fiches.show:120schoolap
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 20. view::public.fiches.show:120
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `oldt_domains` where `oldt_domains`.`id` = 1 and `oldt_domains`.`id` is not null limit 1
        400μsview::public.fiches.show:120schoolap
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 20. view::public.fiches.show:120
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `oldt_sections` where `oldt_sections`.`id` = 3 limit 1
        450μsview::public.fiches.show:136schoolap
        Metadata
        Bindings
        • 0. 3
        Backtrace
        • 20. view::public.fiches.show:136
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `oldt_material_sheet_contents` where `material_sheet_id` = 2094 and `activity` = 0
        32.81ms/app/Models/Old/MaterialSheet.php:73schoolap
        Metadata
        Bindings
        • 0. 2094
        • 1. 0
        Backtrace
        • 14. /app/Models/Old/MaterialSheet.php:73
        • 15. view::public.fiches.show:191
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `oldt_material_sheet_contents` where `material_sheet_id` = 2094 and `activity` = 1
        33.49ms/app/Models/Old/MaterialSheet.php:73schoolap
        Metadata
        Bindings
        • 0. 2094
        • 1. 1
        Backtrace
        • 14. /app/Models/Old/MaterialSheet.php:73
        • 15. view::public.fiches.show:203
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `oldt_material_sheet_contents` where `material_sheet_id` = 2094 and `activity` = 2
        40.7ms/app/Models/Old/MaterialSheet.php:73schoolap
        Metadata
        Bindings
        • 0. 2094
        • 1. 2
        Backtrace
        • 14. /app/Models/Old/MaterialSheet.php:73
        • 15. view::public.fiches.show:214
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      App\Models\Old\MaterialSheetContent
      5
      App\Models\Old\Section
      1
      App\Models\Old\Domain
      1
      App\Models\Old\SubDomain
      1
      App\Models\Old\Discipline
      1
      App\Models\Old\Option
      1
      App\Models\Old\Grade
      1
      App\Models\Old\MaterialSheet
      1
      App\Models\Lesson\Lesson
      1
      App\Models\Old\Post
      5
        _token
        wmspP0DQsbH1kKVPXNPxPhs3N9rw6Dwoc4lf3VKa
        applocale
        en
        _previous
        array:1 [ "url" => "https://s8.schoolap.com/fiches/2478/fractions-irrationnelles" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /fiches/2478/fractions-irrationnelles
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:17 [ "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "connection" => array:1 [ 0 => "keep-alive" ] "host" => array:1 [ 0 => "s8.schoolap.com" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
        request_server
        0 of 0
        array:41 [ "USER" => "www-data" "HOME" => "/var/www" "HTTP_ACCEPT_ENCODING" => "gzip, deflate, br, zstd" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_CONNECTION" => "keep-alive" "HTTP_HOST" => "s8.schoolap.com" "REDIRECT_STATUS" => "200" "SERVER_NAME" => "s8.schoolap.com" "SERVER_PORT" => "443" "SERVER_ADDR" => "188.166.147.66" "REMOTE_PORT" => "40208" "REMOTE_ADDR" => "3.135.229.106" "SERVER_SOFTWARE" => "nginx/1.18.0" "GATEWAY_INTERFACE" => "CGI/1.1" "HTTPS" => "on" "REQUEST_SCHEME" => "https" "SERVER_PROTOCOL" => "HTTP/1.1" "DOCUMENT_ROOT" => "/var/www/s8.schoolap.com/public" "DOCUMENT_URI" => "/index.php" "REQUEST_URI" => "/fiches/2478/fractions-irrationnelles" "SCRIPT_NAME" => "/index.php" "CONTENT_LENGTH" => "" "CONTENT_TYPE" => "" "REQUEST_METHOD" => "GET" "QUERY_STRING" => "" "SCRIPT_FILENAME" => "/var/www/s8.schoolap.com/public/index.php" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/index.php" "REQUEST_TIME_FLOAT" => 1747025836.3667 "REQUEST_TIME" => 1747025836 ]
        request_cookies
        []
        
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Mon, 12 May 2025 04:57:16 GMT" ] "set-cookie" => array:3 [ 0 => "lang_schoolap=eyJpdiI6Ikt5NGpGYnk2WEQxWlpRTmNXMmtQL1E9PSIsInZhbHVlIjoiYkdxTm9YaUVXejhoMjJXMyt6WjBlZ2J2OFZJR2ZEeGVQcUVlT2RkTGZUQTFhczQ4MWlHQm5XaUxoWWJmZE91MyIsIm1hYyI6ImU2ZjJjMjY5Zjc4OTVhYjlhZTcxMDUzNWM1OTEyNTg3M2VjNDdiN2JmMWRlMjEzMzM1MmY5YTM1MWQzYjFhYzciLCJ0YWciOiIifQ%3D%3D; expires=Mon, 19 May 2025 03:37:16 GMT; Max-Age=600000; path=/; httponly; samesite=laxlang_schoolap=eyJpdiI6Ikt5NGpGYnk2WEQxWlpRTmNXMmtQL1E9PSIsInZhbHVlIjoiYkdxTm9YaUVXejhoMjJXMyt6WjBlZ2J2OFZJR2ZEeGVQcUVlT2RkTGZUQTFhczQ4MWlHQm5XaUxoWWJmZE91MyIsIm" 1 => "XSRF-TOKEN=eyJpdiI6InZ4cm1WWmtJTW1tSWhRQzFwdnJyNFE9PSIsInZhbHVlIjoicVZ5aWpIZ0FXZDMrUDNpa3dWTWYvMDBLUGVnTGh4SWo5eVh2UXl4ajVXOU4yak8rbEZRTWJoSnI3WDIrSzJOWEpKeUZUcEhPNjZ3Y2hlWTZ5VjVkd292WjRvcGlLMS9PSVpyZjRpSWxPQzc2TU1rZGdvQXFobjdDNWJ6blZaV04iLCJtYWMiOiI0NjY4NzQ5Y2FiMTkwY2JmNGM0YmZhMTBlNGM3OWRlZjU3NjEwNmZmYjk2MTlhY2FmY2EyYzYxNmQ3OTcwYmE0IiwidGFnIjoiIn0%3D; expires=Mon, 12 May 2025 06:57:16 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6InZ4cm1WWmtJTW1tSWhRQzFwdnJyNFE9PSIsInZhbHVlIjoicVZ5aWpIZ0FXZDMrUDNpa3dWTWYvMDBLUGVnTGh4SWo5eVh2UXl4ajVXOU4yak8rbEZRTWJoSnI3WDIrSzJOWEpKeUZUc" 2 => "schoolap_session=eyJpdiI6Ilh6WVUvNURGN3IxcGhoOVdxOENvU2c9PSIsInZhbHVlIjoicGRIVE9nUWt2OWgwZ3pNTVVHbE5KZ3UvenNYOHVUV0tIckhFRkZpM1A3UUdLc3A3eEZ3MnNsZUpQcjlNQXBOV1VXdlBPVjQvQk9YQVZvQ1ZUQ21ESXVKREtzazZVMHJZTlJ5L2dWNUZpOVRpNjcxWnRIMm4zK1h6Q3g5NHljSGgiLCJtYWMiOiJiYTNlOGU3MTkxZTk1OWMxZjBjZGMxNmE1OWI4Nzk4MGRlYjc4NWY5NDNhY2VmMmY1ODk2ZTNlZTZkYzJhYWE3IiwidGFnIjoiIn0%3D; expires=Mon, 12 May 2025 06:57:16 GMT; Max-Age=7200; path=/; httponly; samesite=laxschoolap_session=eyJpdiI6Ilh6WVUvNURGN3IxcGhoOVdxOENvU2c9PSIsInZhbHVlIjoicGRIVE9nUWt2OWgwZ3pNTVVHbE5KZ3UvenNYOHVUV0tIckhFRkZpM1A3UUdLc3A3eEZ3MnNsZUpQcjlNQXBOV1V" ] "Set-Cookie" => array:3 [ 0 => "lang_schoolap=eyJpdiI6Ikt5NGpGYnk2WEQxWlpRTmNXMmtQL1E9PSIsInZhbHVlIjoiYkdxTm9YaUVXejhoMjJXMyt6WjBlZ2J2OFZJR2ZEeGVQcUVlT2RkTGZUQTFhczQ4MWlHQm5XaUxoWWJmZE91MyIsIm1hYyI6ImU2ZjJjMjY5Zjc4OTVhYjlhZTcxMDUzNWM1OTEyNTg3M2VjNDdiN2JmMWRlMjEzMzM1MmY5YTM1MWQzYjFhYzciLCJ0YWciOiIifQ%3D%3D; expires=Mon, 19-May-2025 03:37:16 GMT; path=/; httponlylang_schoolap=eyJpdiI6Ikt5NGpGYnk2WEQxWlpRTmNXMmtQL1E9PSIsInZhbHVlIjoiYkdxTm9YaUVXejhoMjJXMyt6WjBlZ2J2OFZJR2ZEeGVQcUVlT2RkTGZUQTFhczQ4MWlHQm5XaUxoWWJmZE91MyIsIm" 1 => "XSRF-TOKEN=eyJpdiI6InZ4cm1WWmtJTW1tSWhRQzFwdnJyNFE9PSIsInZhbHVlIjoicVZ5aWpIZ0FXZDMrUDNpa3dWTWYvMDBLUGVnTGh4SWo5eVh2UXl4ajVXOU4yak8rbEZRTWJoSnI3WDIrSzJOWEpKeUZUcEhPNjZ3Y2hlWTZ5VjVkd292WjRvcGlLMS9PSVpyZjRpSWxPQzc2TU1rZGdvQXFobjdDNWJ6blZaV04iLCJtYWMiOiI0NjY4NzQ5Y2FiMTkwY2JmNGM0YmZhMTBlNGM3OWRlZjU3NjEwNmZmYjk2MTlhY2FmY2EyYzYxNmQ3OTcwYmE0IiwidGFnIjoiIn0%3D; expires=Mon, 12-May-2025 06:57:16 GMT; path=/XSRF-TOKEN=eyJpdiI6InZ4cm1WWmtJTW1tSWhRQzFwdnJyNFE9PSIsInZhbHVlIjoicVZ5aWpIZ0FXZDMrUDNpa3dWTWYvMDBLUGVnTGh4SWo5eVh2UXl4ajVXOU4yak8rbEZRTWJoSnI3WDIrSzJOWEpKeUZUc" 2 => "schoolap_session=eyJpdiI6Ilh6WVUvNURGN3IxcGhoOVdxOENvU2c9PSIsInZhbHVlIjoicGRIVE9nUWt2OWgwZ3pNTVVHbE5KZ3UvenNYOHVUV0tIckhFRkZpM1A3UUdLc3A3eEZ3MnNsZUpQcjlNQXBOV1VXdlBPVjQvQk9YQVZvQ1ZUQ21ESXVKREtzazZVMHJZTlJ5L2dWNUZpOVRpNjcxWnRIMm4zK1h6Q3g5NHljSGgiLCJtYWMiOiJiYTNlOGU3MTkxZTk1OWMxZjBjZGMxNmE1OWI4Nzk4MGRlYjc4NWY5NDNhY2VmMmY1ODk2ZTNlZTZkYzJhYWE3IiwidGFnIjoiIn0%3D; expires=Mon, 12-May-2025 06:57:16 GMT; path=/; httponlyschoolap_session=eyJpdiI6Ilh6WVUvNURGN3IxcGhoOVdxOENvU2c9PSIsInZhbHVlIjoicGRIVE9nUWt2OWgwZ3pNTVVHbE5KZ3UvenNYOHVUV0tIckhFRkZpM1A3UUdLc3A3eEZ3MnNsZUpQcjlNQXBOV1V" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "wmspP0DQsbH1kKVPXNPxPhs3N9rw6Dwoc4lf3VKa" "applocale" => "en" "_previous" => array:1 [ "url" => "https://s8.schoolap.com/fiches/2478/fractions-irrationnelles" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]