{"id":224536,"date":"2025-06-03T08:34:18","date_gmt":"2025-06-03T08:34:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224536"},"modified":"2025-06-03T08:34:21","modified_gmt":"2025-06-03T08:34:21","slug":"evaluate-the-square-root-of-21","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/evaluate-the-square-root-of-21\/","title":{"rendered":"Evaluate the square root of 21"},"content":{"rendered":"\n

Evaluate the square root of 21<\/p>\n\n\n\n

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

The square root of 21<\/strong> is approximately: 21\u22484.58257569496\\sqrt{21} \\approx 4.58257569496<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/strong><\/h3>\n\n\n\n

The square root<\/strong> of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3\u00d73=93 \\times 3 = 9.<\/p>\n\n\n\n

Now, 21 is not a perfect square<\/strong>\u2014there is no whole number whose square equals 21. The perfect squares closest to 21 are:<\/p>\n\n\n\n

    \n
  • 42=164^2 = 16<\/li>\n\n\n\n
  • 52=255^2 = 25<\/li>\n<\/ul>\n\n\n\n

    This tells us that: 4<21<54 < \\sqrt{21} < 5<\/p>\n\n\n\n

    To find a more accurate value, we use a numerical approximation method<\/strong>, such as:<\/p>\n\n\n\n

      \n
    • Long division method<\/strong><\/li>\n\n\n\n
    • Newton-Raphson method<\/strong><\/li>\n\n\n\n
    • Using a calculator<\/strong><\/li>\n<\/ul>\n\n\n\n

      With a calculator, we get: 21\u22484.58257569496\\sqrt{21} \\approx 4.58257569496<\/p>\n\n\n\n

      Irrational Nature<\/strong><\/h3>\n\n\n\n

      The square root of 21 is an irrational number<\/strong>. That means:<\/p>\n\n\n\n

        \n
      • It cannot be expressed exactly as a fraction<\/strong>.<\/li>\n\n\n\n
      • Its decimal expansion goes on forever without repeating<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        We can write 21\u22484.5826\\sqrt{21} \\approx 4.5826 if we round to 4 decimal places, which is usually sufficient for most practical purposes.<\/p>\n\n\n\n

        \n\n\n\n

        Applications<\/strong><\/h3>\n\n\n\n

        Understanding square roots is useful in:<\/p>\n\n\n\n

          \n
        • Geometry<\/strong>: For example, calculating the length of a diagonal using the Pythagorean theorem.<\/li>\n\n\n\n
        • Algebra<\/strong>: Solving quadratic equations.<\/li>\n\n\n\n
        • Physics and engineering<\/strong>: Where measurements often involve irrational numbers like 2\\sqrt{2}, 3\\sqrt{3}, or 21\\sqrt{21}.<\/li>\n<\/ul>\n\n\n\n
          \n\n\n\n

          Conclusion<\/strong><\/h3>\n\n\n\n

          While 21\\sqrt{21} cannot be simplified exactly (since 21 has no square factors besides 1), it can be approximated as: 21\u22484.5826\\boxed{\\sqrt{21} \\approx 4.5826}<\/p>\n\n\n\n

          This is the most accurate and practical way to express the square root of 21 in decimal form.<\/p>\n\n\n\n

          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

          Evaluate the square root of 21 The Correct Answer and Explanation is: The square root of 21 is approximately: 21\u22484.58257569496\\sqrt{21} \\approx 4.58257569496 Explanation The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3\u00d73=93 \\times 3 = […]<\/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-224536","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224536","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=224536"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224536\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224536"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224536"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}