{"id":262007,"date":"2025-07-20T10:23:57","date_gmt":"2025-07-20T10:23:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=262007"},"modified":"2025-07-20T10:23:59","modified_gmt":"2025-07-20T10:23:59","slug":"to-which-subsets-of-the-real-numbers-does-the-number-belong","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/20\/to-which-subsets-of-the-real-numbers-does-the-number-belong\/","title":{"rendered":"To which subsets of the real numbers does the number belong"},"content":{"rendered":"\n

To which subsets of the real numbers does the number belong? (square root) 46<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The number 46\\sqrt{46} belongs to the subset of real numbers called irrational numbers<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

The set of real numbers is composed of several subsets, including natural numbers<\/strong>, whole numbers<\/strong>, integers<\/strong>, rational numbers<\/strong>, and irrational numbers<\/strong>. To understand where 46\\sqrt{46} fits, let’s break down each subset:<\/p>\n\n\n\n

    \n
  1. Natural Numbers<\/strong> (N\\mathbb{N}): These are the counting numbers starting from 1 (e.g., 1, 2, 3, …). Since 46\\sqrt{46} is not a whole number, it does not belong to this set.<\/li>\n\n\n\n
  2. Whole Numbers<\/strong>: This set includes all natural numbers and zero (e.g., 0, 1, 2, 3, …). Again, since 46\\sqrt{46} is not an integer, it is not part of this set.<\/li>\n\n\n\n
  3. Integers<\/strong>: The integers consist of all positive and negative whole numbers, including zero (e.g., -3, -2, -1, 0, 1, 2, 3, …). Since 46\\sqrt{46} is not a whole number, it is not an integer either.<\/li>\n\n\n\n
  4. Rational Numbers<\/strong> (Q\\mathbb{Q}): Rational numbers can be written as the quotient of two integers (i.e., in the form ab\\frac{a}{b}, where aa and bb are integers and b\u22600b \\neq 0). 46\\sqrt{46} is not rational because it cannot be expressed as the ratio of two integers. The square root of a non-perfect square is irrational.<\/li>\n\n\n\n
  5. Irrational Numbers<\/strong>: These are real numbers that cannot be expressed as a ratio of two integers. The square root of any prime number, or a non-perfect square, is irrational. 46\\sqrt{46} is an irrational number because it does not have a simple fractional representation. It has an infinite, non-repeating decimal expansion. Specifically, 46\u22486.78233…\\sqrt{46} \\approx 6.78233…, and this decimal continues without repeating.<\/li>\n<\/ol>\n\n\n\n

    Conclusion:<\/h3>\n\n\n\n

    Since 46\\sqrt{46} cannot be expressed as a fraction and has a non-repeating, infinite decimal expansion, it belongs to the subset of irrational numbers<\/strong> within the real numbers.<\/p>\n","protected":false},"excerpt":{"rendered":"

    To which subsets of the real numbers does the number belong? (square root) 46 The correct answer and explanation is: The number 46\\sqrt{46} belongs to the subset of real numbers called irrational numbers. Explanation: The set of real numbers is composed of several subsets, including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-262007","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/262007","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=262007"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/262007\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=262007"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=262007"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=262007"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}