{"id":168381,"date":"2024-11-17T10:45:00","date_gmt":"2024-11-17T10:45:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=168381"},"modified":"2024-11-17T10:45:03","modified_gmt":"2024-11-17T10:45:03","slug":"is-6-23-minus-square-root-2-divided-by-2-rational-or-irrational","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/17\/is-6-23-minus-square-root-2-divided-by-2-rational-or-irrational\/","title":{"rendered":"Is 6\/23 minus square root 2 divided by 2 rational or irrational"},"content":{"rendered":"\n<p>Is 6\/23 minus square root 2 divided by 2 rational or irrational ?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine whether the expression ( \\frac{6}{23} &#8211; \\frac{\\sqrt{2}}{2} ) is rational or irrational, we need to analyze each component of the expression individually and then evaluate how they combine.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Analyze the terms<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>( \\frac{6}{23} ):<\/strong><br>This is a simple fraction, where both the numerator (6) and denominator (23) are integers, and 23 is not equal to zero. Therefore, ( \\frac{6}{23} ) is a rational number. By definition, a number is rational if it can be expressed as a ratio of two integers.<\/li>\n\n\n\n<li><strong>( \\frac{\\sqrt{2}}{2} ):<\/strong><br>The square root of 2, ( \\sqrt{2} ), is a well-known irrational number. An irrational number cannot be expressed as a ratio of two integers. Since dividing an irrational number by a non-zero integer (in this case, 2) does not make it rational, ( \\frac{\\sqrt{2}}{2} ) is also irrational.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Combine the terms<\/h3>\n\n\n\n<p>The expression we are evaluating is:<\/p>\n\n\n\n<p>[<br>\\frac{6}{23} &#8211; \\frac{\\sqrt{2}}{2}<br>]<\/p>\n\n\n\n<p>Here, we are subtracting a rational number (( \\frac{6}{23} )) from an irrational number (( \\frac{\\sqrt{2}}{2} )). The sum or difference of a rational number and an irrational number is always irrational. This is because the rational number cannot &#8220;cancel out&#8221; the irrationality of the other term. More formally:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let ( r ) represent a rational number and ( i ) represent an irrational number. Then, ( r &#8211; i ) results in an irrational number, since if ( r &#8211; i ) were rational, it would imply that ( i = r &#8211; (r &#8211; i) ), which would mean that the irrational number ( i ) is equal to a rational number, a contradiction.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Conclusion<\/h3>\n\n\n\n<p>Since ( \\frac{6}{23} ) is rational and ( \\frac{\\sqrt{2}}{2} ) is irrational, their difference, ( \\frac{6}{23} &#8211; \\frac{\\sqrt{2}}{2} ), must be <strong>irrational<\/strong>.<\/p>\n\n\n\n<p>Thus, the correct answer is <strong>irrational<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Is 6\/23 minus square root 2 divided by 2 rational or irrational ? The Correct Answer and Explanation is: To determine whether the expression ( \\frac{6}{23} &#8211; \\frac{\\sqrt{2}}{2} ) is rational or irrational, we need to analyze each component of the expression individually and then evaluate how they combine. Step 1: Analyze the terms Step [&hellip;]<\/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-168381","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168381","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=168381"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168381\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168381"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168381"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}