{"id":229576,"date":"2025-06-08T09:43:15","date_gmt":"2025-06-08T09:43:15","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=229576"},"modified":"2025-06-08T09:43:17","modified_gmt":"2025-06-08T09:43:17","slug":"find-the-square-root-of-following-number-by-long-division-method-18225","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/08\/find-the-square-root-of-following-number-by-long-division-method-18225\/","title":{"rendered":"find the square root of following number by long division method ,18225"},"content":{"rendered":"\n
find the square root of following number by long division method ,18225 find the square root of following number by long division method ,18225<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
\u2705 Square Root of 18225 Using Long Division Method<\/strong><\/h3>\n\n\n\n
Let\u2019s find the square root of 18225<\/strong> step by step using the long division method<\/strong>.<\/p>\n\n\n\n\n\n\n\n
\ud83d\udd22 Step 1: Pair the digits<\/h4>\n\n\n\n
Start pairing the digits of 18225 from the right:<\/p>\n\n\n\n
\n
1 82 25 \u2192 we get three pairs: (1), (82), (25)<\/li>\n<\/ul>\n\n\n\n\n\n\n\n
\ud83d\udd22 Step 2: Find the largest square \u2264 first pair<\/h4>\n\n\n\n
So, X = 3 Write 3 next to 1 \u2192 Quotient = 13<\/p>\n\n\n\n
Now:<\/p>\n\n\n\n
\n
Subtract: 82 – 69 = 13<\/li>\n\n\n\n
Bring down next pair: 25<\/strong> \u2192 Now working on 1325<\/strong><\/li>\n<\/ul>\n\n\n\n\n\n\n\n
\ud83d\udd22 Step 4: Double the quotient<\/h4>\n\n\n\n
Current quotient = 13 \u2192 Double = 26<\/strong><\/p>\n\n\n\n
We now find X such that: (260 + X) \u00d7 X \u2264 1325<\/strong><\/p>\n\n\n\n
Try:<\/p>\n\n\n\n
\n
X = 5 \u2192 265 \u00d7 5 = 1325 \u2705<\/li>\n<\/ul>\n\n\n\n
So, X = 5 Final quotient = 135<\/strong><\/p>\n\n\n\n
Now:<\/p>\n\n\n\n
\n
Subtract: 1325 – 1325 = 0 \u2192 No remainder<\/li>\n<\/ul>\n\n\n\n\n\n\n\n
\u2705 Final Answer:<\/h3>\n\n\n\n
\u221a18225 = 135<\/strong><\/p>\n\n\n\n\n\n\n\n
\ud83d\udcd8 Explanation<\/h3>\n\n\n\n
The long division method<\/strong> is a systematic process used to find the square root of large numbers without using a calculator. It is especially helpful when perfect squares are involved, like 18225.<\/p>\n\n\n\n
We begin by pairing digits<\/strong> of the number from right to left. For 18225, we group it as (1)(82)(25). These pairs help us break the number into manageable parts as we work through the root step by step.<\/p>\n\n\n\n
We then find the largest square<\/strong> that fits into the first group (1). Since 1 is a perfect square, we start with 1. This becomes the first digit of our answer. After subtracting and bringing down the next pair (82), we proceed to the next stage.<\/p>\n\n\n\n
We now double the root found so far<\/strong> (1 becomes 2), and find a digit (say X) that, when added to 20 (making 20 + X), and then multiplied by X, gives a product close to or equal to the current number (82). We find that 3 fits because 23 \u00d7 3 = 69. This 3 becomes the next digit in the square root.<\/p>\n\n\n\n
We repeat this process for the next pair. Double 13 (which is our current root so far), giving 26. Now, we look for X such that (260 + X) \u00d7 X is as close to 1325 as possible. X = 5 works perfectly here.<\/p>\n\n\n\n
Once the entire number is exhausted and no remainder remains, the digits collected (135) form the square root. Hence, the square root of 18225 is 135<\/strong>.<\/p>\n\n\n\n
This method is reliable and provides a clear, step-by-step approach for perfect square roots.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
find the square root of following number by long division method ,18225find the square root of following number by long division method ,18225 The Correct Answer and Explanation is: \u2705 Square Root of 18225 Using Long Division Method Let\u2019s find the square root of 18225 step by step using the long division method. \ud83d\udd22 Step […]<\/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-229576","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229576","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=229576"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229576\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=229576"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=229576"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=229576"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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