{"id":223211,"date":"2025-06-01T10:49:01","date_gmt":"2025-06-01T10:49:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223211"},"modified":"2025-06-01T10:49:03","modified_gmt":"2025-06-01T10:49:03","slug":"find-square-root-of-15-25-by-division-method-upto-3-decimal","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/01\/find-square-root-of-15-25-by-division-method-upto-3-decimal\/","title":{"rendered":"find square root of 15.25 by division method upto 3 decimal"},"content":{"rendered":"\n

find square root of 15.25 by division method upto 3 decimal<\/p>\n\n\n\n

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

\u221a15.25 by Division Method (up to 3 decimal places)<\/h3>\n\n\n\n

We will now find the square root of 15.25 using the long division method<\/strong>, step-by-step.<\/p>\n\n\n\n

\n\n\n\n

\u2705 Answer:<\/strong><\/h3>\n\n\n\n

\u221a15.25 \u2248 3.905<\/strong> (correct to 3 decimal places)<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udcd8 Explanation<\/h3>\n\n\n\n

The long division method is a traditional technique used to find square roots of numbers (especially non-perfect squares) up to a desired number of decimal places. It is particularly useful when calculators are not allowed, such as in exams.<\/p>\n\n\n\n

Here is how we find \u221a15.25 step by step:<\/p>\n\n\n\n

1. Group the Digits:<\/strong><\/h4>\n\n\n\n
    \n
  • Write 15.25 as 15.25 00 00 (adding pairs of zeros for decimal places).<\/li>\n\n\n\n
  • Group digits in pairs from the decimal point: 15 | 25 | 00 | 00<\/strong><\/li>\n<\/ul>\n\n\n\n

    2. Find the Largest Square \u2264 First Group (15):<\/strong><\/h4>\n\n\n\n
      \n
    • 3\u00b2 = 9 and 4\u00b2 = 16 \u2192 use 3<\/li>\n\n\n\n
    • Put 3 as the first digit of the root.<\/li>\n\n\n\n
    • Subtract 9 from 15 \u2192 remainder = 6<\/li>\n\n\n\n
    • Bring down next pair \u2192 new dividend = 625<\/li>\n<\/ul>\n\n\n\n

      3. Double the root (3 \u2192 6), find next digit (D):<\/strong><\/h4>\n\n\n\n
        \n
      • Try (60 + D) \u00d7 D \u2264 625<\/li>\n\n\n\n
      • Try D = 9: (60 + 9) \u00d7 9 = 69 \u00d7 9 = 621<\/li>\n\n\n\n
      • It’s valid \u2192 next digit is 9<\/li>\n\n\n\n
      • Root so far = 3.9<\/strong><\/li>\n\n\n\n
      • Subtract: 625 – 621 = 4<\/li>\n\n\n\n
      • Bring down next pair \u2192 400<\/li>\n<\/ul>\n\n\n\n

        4. Double root (3.9 \u2192 78), find next digit:<\/strong><\/h4>\n\n\n\n
          \n
        • Try (780 + D) \u00d7 D \u2264 400<\/li>\n\n\n\n
        • Try D = 0 \u2192 780 \u00d7 0 = 0 \u2192 fits<\/li>\n\n\n\n
        • Next digit = 0 \u2192 Root = 3.90<\/strong><\/li>\n\n\n\n
        • Subtract: 400 – 0 = 400<\/li>\n\n\n\n
        • Bring down next pair \u2192 40000<\/li>\n<\/ul>\n\n\n\n

          5. Double root (3.90 \u2192 780), find D:<\/strong><\/h4>\n\n\n\n
            \n
          • Try D = 5: (7800 + 5) \u00d7 5 = 7805 \u00d7 5 = 39025<\/li>\n\n\n\n
          • Fits \u2192 next digit is 5<\/li>\n\n\n\n
          • Final root = 3.905<\/strong><\/li>\n<\/ul>\n\n\n\n

            Hence, \u221a15.25 \u2248 3.905<\/strong> (correct up to 3 decimal places).<\/p>\n\n\n\n

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

            find square root of 15.25 by division method upto 3 decimal The Correct Answer and Explanation is: \u221a15.25 by Division Method (up to 3 decimal places) We will now find the square root of 15.25 using the long division method, step-by-step. \u2705 Answer: \u221a15.25 \u2248 3.905 (correct to 3 decimal places) \ud83d\udcd8 Explanation The long […]<\/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-223211","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223211","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=223211"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223211\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223211"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223211"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223211"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}