{"id":245058,"date":"2025-07-05T16:23:27","date_gmt":"2025-07-05T16:23:27","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245058"},"modified":"2025-07-05T16:23:29","modified_gmt":"2025-07-05T16:23:29","slug":"a-factor-tree-branches-down-into-2-branches","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/05\/a-factor-tree-branches-down-into-2-branches\/","title":{"rendered":"A factor tree branches down into 2 branches."},"content":{"rendered":"\n
A factor tree branches down into 2 branches. The first number 1,225 branches down on the left to 5 and on the right to 245. 245 branches down to 5 on the left and 49 on the right. 49 branches down to 7 on the left and 7 on the right. A factor tree is shown for 1,225. What is the simplest form of \u00e2\u02c6\u01611,225?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
To simplify 1,225\\sqrt{1,225}1,225\u200b, we can use the factor tree that you’ve described. Let’s break it down step by step:<\/p>\n\n\n\n
Factor Tree Breakdown:<\/h3>\n\n\n\n
\n
1,225 branches down into 5 on the left and 245 on the right.<\/strong> 1,225=5\u00d72451,225 = 5 \\times 2451,225=5\u00d7245<\/li>\n\n\n\n
245 branches down into 5 on the left and 49 on the right.<\/strong> 245=5\u00d749245 = 5 \\times 49245=5\u00d749<\/li>\n\n\n\n
49 branches down into 7 on the left and 7 on the right.<\/strong> 49=7\u00d7749 = 7 \\times 749=7\u00d77<\/li>\n<\/ul>\n\n\n\n
Full Prime Factorization:<\/h3>\n\n\n\n
From the tree, we can express 1,2251,2251,225 as:1,225=5\u00d75\u00d75\u00d77\u00d771,225 = 5 \\times 5 \\times 5 \\times 7 \\times 71,225=5\u00d75\u00d75\u00d77\u00d77<\/p>\n\n\n\n
This simplifies to:1,225=53\u00d7721,225 = 5^3 \\times 7^21,225=53\u00d772<\/p>\n\n\n\n
Simplifying the Square Root:<\/h3>\n\n\n\n
Now, to simplify 1,225\\sqrt{1,225}1,225\u200b, we use the property of square roots that a\u00d7b=a\u00d7b\\sqrt{a \\times b} = \\sqrt{a} \\times \\sqrt{b}a\u00d7b\u200b=a\u200b\u00d7b\u200b. Applying this to the factorization:1,225=53\u00d772\\sqrt{1,225} = \\sqrt{5^3 \\times 7^2}1,225\u200b=53\u00d772\u200b<\/p>\n\n\n\n
We can split the square root into two parts:1,225=52\u00d75\u00d772=52\u00d772\u00d75\\sqrt{1,225} = \\sqrt{5^2 \\times 5 \\times 7^2} = \\sqrt{5^2} \\times \\sqrt{7^2} \\times \\sqrt{5}1,225\u200b=52\u00d75\u00d772\u200b=52\u200b\u00d772\u200b\u00d75\u200b<\/p>\n\n\n\n
Since 52=5\\sqrt{5^2} = 552\u200b=5 and 72=7\\sqrt{7^2} = 772\u200b=7, this simplifies to:1,225=5\u00d77\u00d75=355\\sqrt{1,225} = 5 \\times 7 \\times \\sqrt{5} = 35 \\sqrt{5}1,225\u200b=5\u00d77\u00d75\u200b=355\u200b<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
The simplest form of 1,225\\sqrt{1,225}1,225\u200b is:355\\boxed{35\\sqrt{5}}355\u200b\u200b<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
The square root of 1,2251,2251,225 cannot be simplified further because 5\\sqrt{5}5\u200b is an irrational number. Thus, the simplest exact form is 35535\\sqrt{5}355\u200b, which provides a clean representation of the square root.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
A factor tree branches down into 2 branches. The first number 1,225 branches down on the left to 5 and on the right to 245. 245 branches down to 5 on the left and 49 on the right. 49 branches down to 7 on the left and 7 on the right. A factor tree is […]<\/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-245058","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245058","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=245058"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245058\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245058"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245058"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245058"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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