To solve this problem, we will break it down step by step.<\/p>\n\n\n\n
Step 1: Simplify the expression inside the square root<\/h3>\n\n\n\n
We start with:90+80\\sqrt{90} + \\sqrt{80}90\u200b+80\u200b<\/p>\n\n\n\n
First, simplify each square root:90=9\u00d710=310\\sqrt{90} = \\sqrt{9 \\times 10} = 3\\sqrt{10}90\u200b=9\u00d710\u200b=310\u200b80=16\u00d75=45\\sqrt{80} = \\sqrt{16 \\times 5} = 4\\sqrt{5}80\u200b=16\u00d75\u200b=45\u200b<\/p>\n\n\n\n
So, we now have:90+80=310+45\\sqrt{90} + \\sqrt{80} = 3\\sqrt{10} + 4\\sqrt{5}90\u200b+80\u200b=310\u200b+45\u200b<\/p>\n\n\n\n
Step 2: Multiply the sum by 2\u22121\\sqrt{2 – 1}2\u22121\u200b<\/h3>\n\n\n\n
Next, we are asked to multiply this sum by 2\u22121\\sqrt{2 – 1}2\u22121\u200b. Since 2\u22121=12 – 1 = 12\u22121=1, we have:2\u22121=1=1\\sqrt{2 – 1} = \\sqrt{1} = 12\u22121\u200b=1\u200b=1<\/p>\n\n\n\n
Thus, multiplying by 1 does not change the value, so:(310+45)\u00d71=310+45(3\\sqrt{10} + 4\\sqrt{5}) \\times 1 = 3\\sqrt{10} + 4\\sqrt{5}(310\u200b+45\u200b)\u00d71=310\u200b+45\u200b<\/p>\n\n\n\n
Step 3: Raise the product to the power of 4<\/h3>\n\n\n\n
Now, the product is raised to the power of 4. We need to simplify the entire expression 310+453\\sqrt{10} + 4\\sqrt{5}310\u200b+45\u200b raised to the power of 4. However, we must note that:(310+45)4(3\\sqrt{10} + 4\\sqrt{5})^4(310\u200b+45\u200b)4<\/p>\n\n\n\n
This is a bit more complex. Rather than expanding manually, let\u2019s estimate each square root value for a rough result:10\u22483.162\\sqrt{10} \\approx 3.16210\u200b\u22483.1625\u22482.236\\sqrt{5} \\approx 2.2365\u200b\u22482.236<\/p>\n\n\n\n
So,310\u22483\u00d73.162=9.4863\\sqrt{10} \\approx 3 \\times 3.162 = 9.486310\u200b\u22483\u00d73.162=9.48645\u22484\u00d72.236=8.9444\\sqrt{5} \\approx 4 \\times 2.236 = 8.94445\u200b\u22484\u00d72.236=8.944<\/p>\n\n\n\n
Thus:310+45\u22489.486+8.944=18.433\\sqrt{10} + 4\\sqrt{5} \\approx 9.486 + 8.944 = 18.43310\u200b+45\u200b\u22489.486+8.944=18.43<\/p>\n\n\n\n
Now, raise this to the power of 4:(18.43)4\u224818443.62\u2248339,141,304(18.43)^4 \\approx 18443.6^2 \\approx 339,141,304(18.43)4\u224818443.62\u2248339,141,304<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
The result of raising the expression to the power of 4 is approximately 339,141,304<\/strong>.<\/p>\n\n\n\n If the positive square root of (root 90 + root 80 ) is multiplied by (root (2 -1)) and the product is raised to the power of four, the result would be The Correct Answer and Explanation is: To solve this problem, we will break it down step by step. Step 1: Simplify the expression […]<\/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-259472","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259472","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=259472"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259472\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=259472"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=259472"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=259472"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-974.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"