The square root of 2 is an irrational number<\/strong>.<\/p>\n\n\n\n To explain why, we can use a proof by contradiction. Let\u2019s assume that the square root of 2 is rational. This means it can be expressed as the ratio of two integers, say:2=ab\\sqrt{2} = \\frac{a}{b}2\u200b=ba\u200b<\/p>\n\n\n\n where aaa and bbb are integers, and aaa and bbb have no common factors (i.e., the fraction is in its simplest form). Squaring both sides, we get:2=a2b22 = \\frac{a^2}{b^2}2=b2a2\u200b<\/p>\n\n\n\n Multiplying both sides by b2b^2b2, we get:2b2=a22b^2 = a^22b2=a2<\/p>\n\n\n\n This equation tells us that a2a^2a2 is an even number because it is equal to 2b22b^22b2. If a2a^2a2 is even, then aaa must also be even, since the square of an odd number is odd.<\/p>\n\n\n\n Let\u2019s now express aaa as a=2ka = 2ka=2k, where kkk is an integer. Substituting this back into the equation 2b2=a22b^2 = a^22b2=a2, we get:2b2=(2k)2=4k22b^2 = (2k)^2 = 4k^22b2=(2k)2=4k2<\/p>\n\n\n\n Dividing both sides by 2:b2=2k2b^2 = 2k^2b2=2k2<\/p>\n\n\n\n This shows that b2b^2b2 is also even, and therefore, bbb must also be even.<\/p>\n\n\n\n Now, we have shown that both aaa and bbb are even, which contradicts our assumption that they have no common factors (because both are divisible by 2). Therefore, the assumption that 2\\sqrt{2}2\u200b is rational must be false.<\/p>\n\n\n\n Since 2\\sqrt{2}2\u200b cannot be written as the ratio of two integers, it is irrational<\/strong>.<\/p>\n\n\n\n Is the square root of 2 rational or irrational? The Correct Answer and Explanation is: The square root of 2 is an irrational number. To explain why, we can use a proof by contradiction. Let\u2019s assume that the square root of 2 is rational. This means it can be expressed as the ratio of two […]<\/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-264096","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264096","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=264096"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264096\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=264096"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=264096"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=264096"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1367.jpeg\")
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