{"id":271352,"date":"2025-07-25T17:58:17","date_gmt":"2025-07-25T17:58:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271352"},"modified":"2025-07-25T17:58:20","modified_gmt":"2025-07-25T17:58:20","slug":"which-of-the-following-numbers-has-irrational-square-root","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/25\/which-of-the-following-numbers-has-irrational-square-root\/","title":{"rendered":"Which of the following numbers has irrational square root"},"content":{"rendered":"\n

. Which of the following numbers has irrational square root? * 64 25 0.1<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The number that has an irrational square root among the options is 0.1<\/strong>.<\/p>\n\n\n\n

Here’s why:<\/h3>\n\n\n\n
    \n
  1. 64<\/strong>:\n
      \n
    • The square root of 64 is 8<\/strong>, because 64=8\\sqrt{64} = 864\u200b=8. This is a rational number, as it can be expressed as a fraction (8\/1).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • 25<\/strong>:\n
        \n
      • The square root of 25 is 5<\/strong>, because 25=5\\sqrt{25} = 525\u200b=5. This is also a rational number, as it can be expressed as a fraction (5\/1).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • 0.1<\/strong>:\n
          \n
        • The square root of 0.1 is approximately 0.316227766…<\/strong>, which is a non-repeating, non-terminating decimal. This is an example of an irrational number<\/strong>. Irrational numbers cannot be written as exact fractions of integers, and their decimal expansion goes on forever without repeating.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

          What makes 0.1\u2019s square root irrational?<\/h3>\n\n\n\n

          The key to identifying irrational numbers is whether their square root results in a non-repeating and non-terminating decimal. In this case, 0.1\\sqrt{0.1}0.1\u200b has a decimal expansion that neither terminates nor repeats, which satisfies the definition of an irrational number.<\/p>\n\n\n\n

          On the other hand, numbers like 64 and 25 have square roots that are finite integers, which are rational. Therefore, among the options, 0.1<\/strong> is the number whose square root is irrational.<\/p>\n\n\n\n

          In summary:<\/p>\n\n\n\n

            \n
          • 64=8\\sqrt{64} = 864\u200b=8, a rational number.<\/li>\n\n\n\n
          • 25=5\\sqrt{25} = 525\u200b=5, a rational number.<\/li>\n\n\n\n
          • 0.1\u22480.316227766…\\sqrt{0.1} \\approx 0.316227766…0.1\u200b\u22480.316227766…, an irrational number.<\/li>\n<\/ul>\n\n\n\n
            \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

            . Which of the following numbers has irrational square root? * 64 25 0.1 The Correct Answer and Explanation is: The number that has an irrational square root among the options is 0.1. Here’s why: What makes 0.1\u2019s square root irrational? The key to identifying irrational numbers is whether their square root results in a […]<\/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-271352","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271352","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=271352"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271352\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271352"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271352"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271352"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}