{"id":238543,"date":"2025-06-18T08:05:59","date_gmt":"2025-06-18T08:05:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=238543"},"modified":"2025-06-18T08:06:02","modified_gmt":"2025-06-18T08:06:02","slug":"what-is-the-square-root-of-1000-by-long-division-method-full-solution","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/18\/what-is-the-square-root-of-1000-by-long-division-method-full-solution\/","title":{"rendered":"What is the square root of 1000 by long division method full solution"},"content":{"rendered":"\n

What is the square root of 1000 by long division method full solution.<\/p>\n\n\n\n

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

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

The square root of 1000 by long division method is approximately 31.62<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

\u2705 Step-by-Step Long Division Method:<\/h3>\n\n\n\n

Step 1: Group the digits of 1000 in pairs from right to left.<\/h4>\n\n\n\n

We write 1000 as 10 | 00<\/strong> (grouped from right).<\/p>\n\n\n\n

Step 2: Find the largest number whose square is less than or equal to the first group (10).<\/h4>\n\n\n\n
    \n
  • 32=93^2 = 932=9 and 42=164^2 = 1642=16 which is greater than 10<\/li>\n\n\n\n
  • So we take 3<\/strong> as the first digit of the square root<\/li>\n\n\n\n
  • Subtract 999 from 101010: 10\u22129=110 – 9 = 110\u22129=1<\/li>\n<\/ul>\n\n\n\n

    Step 3: Bring down the next pair (00) next to 1. Now we have 100<\/strong>.<\/h4>\n\n\n\n
      \n
    • Double the quotient found so far (3) \u2192 3\u00d72=63 \\times 2 = 63\u00d72=6<\/li>\n\n\n\n
    • We now look for a digit X such that 6X\u00d7X\u22641006X \\times X \\leq 1006X\u00d7X\u2264100<\/li>\n<\/ul>\n\n\n\n

      Try:<\/p>\n\n\n\n

        \n
      • 61\u00d71=6161 \\times 1 = 6161\u00d71=61<\/li>\n\n\n\n
      • 62\u00d72=12462 \\times 2 = 12462\u00d72=124 which is too big<\/li>\n<\/ul>\n\n\n\n

        So we choose 1<\/strong>, and our divisor becomes 61<\/p>\n\n\n\n

          \n
        • Subtract 616161 from 100100100: 100\u221261=39100 – 61 = 39100\u221261=39<\/li>\n<\/ul>\n\n\n\n

          Step 4: Bring down two zeros (assume we want decimal places). Now we have 3900<\/strong>.<\/h4>\n\n\n\n
            \n
          • New quotient so far is 31<\/li>\n\n\n\n
          • Double 31 \u2192 626262<\/li>\n<\/ul>\n\n\n\n

            Try:<\/p>\n\n\n\n

              \n
            • 621\u00d71=621621 \\times 1 = 621621\u00d71=621<\/li>\n\n\n\n
            • 622\u00d72=1244622 \\times 2 = 1244622\u00d72=1244<\/li>\n\n\n\n
            • 625\u00d75=3125625 \\times 5 = 3125625\u00d75=3125<\/li>\n\n\n\n
            • 626\u00d76=3756626 \\times 6 = 3756626\u00d76=3756<\/li>\n\n\n\n
            • 627\u00d77=4389627 \\times 7 = 4389627\u00d77=4389 which is too much<\/li>\n<\/ul>\n\n\n\n

              So take 6<\/strong><\/p>\n\n\n\n

                \n
              • Add 6 to divisor to make it 626<\/li>\n\n\n\n
              • 626\u00d76=3756626 \\times 6 = 3756626\u00d76=3756<\/li>\n\n\n\n
              • Subtract: 3900\u22123756=1443900 – 3756 = 1443900\u22123756=144<\/li>\n<\/ul>\n\n\n\n

                So far, our square root is 31.6<\/strong><\/p>\n\n\n\n

                Step 5: Continue for more decimal places if needed<\/h4>\n\n\n\n

                Bring down two zeros to get 14400
                Double 316 = 632<\/p>\n\n\n\n

                Try:<\/p>\n\n\n\n

                  \n
                • 6322\u00d72=126446322 \\times 2 = 126446322\u00d72=12644<\/li>\n\n\n\n
                • 6323\u00d73=189696323 \\times 3 = 189696323\u00d73=18969 too much<\/li>\n<\/ul>\n\n\n\n

                  So take 2<\/strong><\/p>\n\n\n\n

                    \n
                  • 6322\u00d72=126446322 \\times 2 = 126446322\u00d72=12644<\/li>\n\n\n\n
                  • Subtract: 14400\u221212644=175614400 – 12644 = 175614400\u221212644=1756<\/li>\n<\/ul>\n\n\n\n

                    So square root of 1000 \u2248 31.62<\/strong><\/p>\n\n\n\n

                    \n\n\n\n

                    \u2705 Explanation<\/h3>\n\n\n\n

                    The square root of 1000 can be found using the long division method. This approach is helpful when calculators are not allowed or when we want to find a root to a specific number of decimal places. The method works by repeatedly dividing in a way similar to regular long division, but with a focus on estimating square values step by step.<\/p>\n\n\n\n

                    We start by pairing the digits of 1000 from the right. This gives us two pairs: 10 and 00. We find the square root of the first pair, which is 10. The square root of 10 is between 3 and 4, so we take 3. We square it and subtract the result from 10, leaving us with a remainder. We then bring down the next pair of digits to continue the process.<\/p>\n\n\n\n

                    Next, we double the current quotient (3 becomes 6), then find a digit which, when added to 60 and multiplied by itself, gives a product less than or equal to the current dividend. We repeat this process: double the quotient, estimate the next digit, multiply, subtract, and bring down more digits as needed.<\/p>\n\n\n\n

                    Each step brings us closer to the actual square root, digit by digit. This method works because it mirrors the algebraic process of finding square roots by estimating one digit at a time, based on what is already known.<\/p>\n\n\n\n

                    Using this method, the square root of 1000 comes out to approximately 31.62<\/strong>, and you can continue the process further if more precision is needed. The result is a non-repeating, non-terminating decimal, because 1000 is not a perfect square.<\/p>\n\n\n\n

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

                    What is the square root of 1000 by long division method full solution. The Correct Answer and Explanation is: \u2705 Correct Answer: The square root of 1000 by long division method is approximately 31.62. \u2705 Step-by-Step Long Division Method: Step 1: Group the digits of 1000 in pairs from right to left. We write 1000 […]<\/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-238543","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238543","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=238543"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238543\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}