{"id":223210,"date":"2025-06-16T07:48:47","date_gmt":"2025-06-16T07:48:47","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223210"},"modified":"2025-06-16T07:48:49","modified_gmt":"2025-06-16T07:48:49","slug":"find-square-root-of-15-25-by-division-method-upto-3-decimal-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/find-square-root-of-15-25-by-division-method-upto-3-decimal-2\/","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

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

The square root of 15.25<\/strong> using the long division method<\/strong> up to three decimal places<\/strong> is:<\/p>\n\n\n\n

\u221a15.25 \u2248 3.905<\/strong><\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd0d Step-by-Step Explanation (Long Division Method):<\/strong><\/h3>\n\n\n\n
    \n
  1. Pair the Digits:<\/strong>
    Start by placing the number in pairs from the decimal point.\n
      \n
    • 15.25 \u2192 Pair as: (15)(25)<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Find Initial Root:<\/strong>\n
        \n
      • Find the largest number whose square is \u2264 15.<\/li>\n\n\n\n
      • 3\u00b2 = 9 and 4\u00b2 = 16 \u2192 So choose 3.<\/li>\n\n\n\n
      • Write 3 as the first digit of the square root.<\/li>\n\n\n\n
      • Subtract 9 from 15:
        15 \u2212 9 = 6<\/li>\n\n\n\n
      • Bring down next pair (25): Now we have 625<\/strong>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Double the Quotient:<\/strong>\n
          \n
        • Double of 3 = 6. Write it as a divisor prefix.<\/li>\n\n\n\n
        • Try numbers like 61\u00d71 = 61, 62\u00d72 = 124, …, 69\u00d79 = 621<\/li>\n\n\n\n
        • 69\u00d79 = 621 \u2264 625<\/li>\n\n\n\n
        • Choose 9<\/li>\n\n\n\n
        • Write 9 as the next digit after decimal: 3.9<\/strong><\/li>\n\n\n\n
        • Subtract 621 from 625 \u2192 remainder = 4<\/li>\n\n\n\n
        • Bring down next pair (00): Now you have 400<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • Repeat the Process:<\/strong>\n
            \n
          • Double 39 = 78. Use 78_ as divisor.<\/li>\n\n\n\n
          • Try 781\u00d71 = 781, 782\u00d72 = 1564, …, 785\u00d75 = 3925<\/li>\n\n\n\n
          • 785\u00d75 = 3925 \u2264 4000<\/li>\n\n\n\n
          • Choose 5<\/li>\n\n\n\n
          • Write 5: \u221a15.25 = 3.90<\/strong>5<\/li>\n\n\n\n
          • Subtract 3925 from 4000 = 75<\/li>\n\n\n\n
          • Bring down next pair (00): Now 7500<\/li>\n<\/ul>\n<\/li>\n\n\n\n
          • Continue:<\/strong>\n
              \n
            • Double 3905 = 7810<\/li>\n\n\n\n
            • Try 78101\u00d71 = 78101, too big.<\/li>\n\n\n\n
            • 7801\u00d71 = 7801, too big \u2192 Try 780\u00d70 = 0<\/li>\n\n\n\n
            • We stop at 3 decimal places: \u221a15.25 \u2248 3.905<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
              \n\n\n\n

              \ud83d\udcd8 Conclusion:<\/strong><\/h3>\n\n\n\n

              The square root of 15.25<\/strong> using the long division method<\/strong> up to three decimal places<\/strong> is 3.905<\/strong>. This method breaks down square roots step-by-step, ensuring precise manual calculation without a calculator. It\u2019s especially helpful in exams or competitive tests where calculators are not allowed.<\/p>\n","protected":false},"excerpt":{"rendered":"

              Find square root of 15.25 by division method upto 3 decimal The Correct Answer and Explanation is: Correct Answer: The square root of 15.25 using the long division method up to three decimal places is: \u221a15.25 \u2248 3.905 \ud83d\udd0d Step-by-Step Explanation (Long Division Method): \ud83d\udcd8 Conclusion: The square root of 15.25 using the long division […]<\/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-223210","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223210","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=223210"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223210\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223210"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}