{"id":37409,"date":"2025-06-25T18:54:51","date_gmt":"2025-06-25T18:54:51","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=37409"},"modified":"2025-06-25T18:54:53","modified_gmt":"2025-06-25T18:54:53","slug":"find-that-square-root-12-square-root-13-is-irrational-number","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-that-square-root-12-square-root-13-is-irrational-number\/","title":{"rendered":"Find that square root 12 \/square root 13 is irrational number"},"content":{"rendered":"\n<p>Find that square root 12 \/square root 13 is irrational number<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Yes, the expression \u221a12 \/ \u221a13 is an <strong>irrational number<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To understand why \u221a12 \/ \u221a13 is irrational, start by simplifying the expression: 1213=1213\\frac{\\sqrt{12}}{\\sqrt{13}} = \\sqrt{\\frac{12}{13}}<\/p>\n\n\n\n<p>Now consider whether the number inside the square root, <strong>12\/13<\/strong>, is a perfect square. A number is a perfect square if it can be expressed as the square of a <strong>rational number<\/strong>. In this case, 12 and 13 are both integers, but their ratio is <strong>not<\/strong> a perfect square. This is because:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>12 is not a multiple of 13<\/li>\n\n\n\n<li>13 is a <strong>prime number<\/strong>, and 12 does not include 13 as a factor<\/li>\n\n\n\n<li>12\/13 is a <strong>rational<\/strong> number, but it is <strong>not<\/strong> a perfect square<\/li>\n<\/ul>\n\n\n\n<p>Since 12\/13 is not a perfect square, its square root, \u221a(12\/13), <strong>cannot be a rational number<\/strong>.<\/p>\n\n\n\n<p>In general, the square root of a <strong>non-perfect square rational number<\/strong> is <strong>always irrational<\/strong>. That means \u221a(12\/13) is irrational. Therefore, the original expression \u221a12 \/ \u221a13, which is equal to \u221a(12\/13), is also irrational.<\/p>\n\n\n\n<p>Another way to see this is by considering the definitions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A rational number can be expressed as a fraction of two integers a\/b, where b is not zero.<\/li>\n\n\n\n<li>An irrational number <strong>cannot<\/strong> be written in that way.<\/li>\n<\/ul>\n\n\n\n<p>If \u221a12 \/ \u221a13 were rational, then squaring both sides would give 12\/13 as a perfect square, but that is false. So, \u221a12 \/ \u221a13 is irrational.<\/p>\n\n\n\n<p>Hence, <strong>\u221a12 \/ \u221a13 is an irrational number<\/strong> because it is the square root of a non-perfect square rational number.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find that square root 12 \/square root 13 is irrational number The correct answer and explanation is: Yes, the expression \u221a12 \/ \u221a13 is an irrational number. Explanation: To understand why \u221a12 \/ \u221a13 is irrational, start by simplifying the expression: 1213=1213\\frac{\\sqrt{12}}{\\sqrt{13}} = \\sqrt{\\frac{12}{13}} Now consider whether the number inside the square root, 12\/13, is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-37409","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37409","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=37409"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37409\/revisions"}],"predecessor-version":[{"id":37410,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37409\/revisions\/37410"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=37409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=37409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=37409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}