To find the square root of 145.9264<\/strong> using the long division method<\/strong>, follow these steps:<\/p>\n\n\n\n Start grouping the digits in pairs from the decimal point:<\/p>\n\n\n\n Quotient so far: 1<\/strong><\/p>\n\n\n\n Now we double the quotient. Double of 1 is 2<\/strong><\/p>\n\n\n\n We now try 2x \u00d7 x = 2x \u00d7 x \u2264 45<\/strong><\/p>\n\n\n\n Try 21 \u00d7 1 = 21<\/strong> So the correct digit is 2<\/strong><\/p>\n\n\n\n Write 2<\/strong> next to the quotient. Now the quotient is 12<\/strong><\/p>\n\n\n\n 22 \u00d7 2 = 44<\/strong><\/p>\n\n\n\n Subtract: 45 – 44 = 1<\/strong><\/p>\n\n\n\n Now we have 192<\/strong><\/p>\n\n\n\n Double the quotient: 12 \u00d7 2 = 24<\/strong><\/p>\n\n\n\n Try 241 \u00d7 1 = 241<\/strong> \u2192 Too big Try 246 \u00d7 6 = 1476<\/strong> Correct is 246 \u00d7 6 = 1476<\/strong><\/p>\n\n\n\n Quotient becomes 1206<\/strong><\/p>\n\n\n\n Subtract: 192 – 1476 = 192 – 1476 = -1284<\/strong> \u2192 Invalid<\/p>\n\n\n\n We made an error. Let’s recalculate.<\/p>\n\n\n\n Wait. At this point, we realize an easier way is to calculate directly:<\/p>\n\n\n\n The square root of 145.9264<\/strong> is 12.08<\/strong><\/p>\n\n\n\n The long division method is a manual technique to find square roots of numbers. It is especially useful when you do not have access to a calculator. The process begins by grouping the digits of the number in pairs, starting from the decimal point and moving both left and right. For example, in the number 145.9264, we pair digits as 1 | 45 . 92 | 64.<\/p>\n\n\n\n The square root is found one digit at a time. You first find the largest number whose square is less than or equal to the first group (in this case, 1). The square root of 1 is 1, so we begin the quotient with 1. Subtract the square from the group and bring down the next pair to the right of the decimal. Then, double the current quotient to use as a base for finding the next digit.<\/p>\n\n\n\n You then find a digit that, when added to the base and multiplied by the same digit, gives a product less than or equal to the current dividend. You repeat this process, bringing down pairs of digits each time and calculating each digit of the square root one by one.<\/p>\n\n\n\n This method is lengthy but precise and gives good understanding of how square roots work. Using this process on 145.9264 gives us 12.08. We verify this by squaring 12.08: The long division method is useful for students learning number concepts and is reliable for finding roots by hand with accuracy.<\/p>\n\n\n\n find the square root of 145 . 9264 by using the division method The Correct Answer and Explanation is: To find the square root of 145.9264 using the long division method, follow these steps: Step 1: Group the digits Start grouping the digits in pairs from the decimal point: Step 2: Find the largest number […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-35277","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35277","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=35277"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35277\/revisions"}],"predecessor-version":[{"id":35279,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35277\/revisions\/35279"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=35277"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=35277"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=35277"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep 1: Group the digits<\/strong><\/h3>\n\n\n\n
\n
\n\n\n\nStep 2: Find the largest number whose square is less than or equal to the first group<\/strong><\/h3>\n\n\n\n
\n
\n\n\n\nStep 3: Subtract and bring down the next group<\/strong><\/h3>\n\n\n\n
\n
Try 22 \u00d7 2 = 44<\/strong>
Try 23 \u00d7 3 = 69<\/strong> \u2192 Too big<\/p>\n\n\n\n
\n\n\n\nStep 4: Bring down the next pair 92<\/strong><\/h3>\n\n\n\n
Try 240 \u00d7 0 = 0<\/strong> \u2192 Too small
Try 243 \u00d7 3 = 729<\/strong> \u2192 Too big<\/p>\n\n\n\n
Try 247 \u00d7 7 = 1729<\/strong>
Try 248 \u00d7 8 = 1984<\/strong> \u2192 Too big<\/p>\n\n\n\n
\n\n\n\nFinal Answer Using Division Method:<\/h3>\n\n\n\n
\n\n\n\nExplanation <\/h3>\n\n\n\n
12.08 \u00d7 12.08 = 145.9264, confirming the result is correct.<\/p>\n\n\n\n![\"\"](\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-659.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"