Let’s break down the given expression step by step:<\/p>\n\n\n\n
The expression is: 2+5(\u2212254)2\u2212(2\u22125+2+5)2\\frac{2 + \\sqrt{5}}{(-254)^2} – (2 – 5 + 2 + 5)^2(\u2212254)22+5\u200b\u200b\u2212(2\u22125+2+5)2<\/p>\n\n\n\n
Step 1: Simplify the numerator in the first term<\/h3>\n\n\n\n
2+52 + \\sqrt{5}2+5\u200b<\/p>\n\n\n\n
This is already in its simplest form, so we leave it as is.<\/p>\n\n\n\n
Step 2: Simplify the denominator in the first term<\/h3>\n\n\n\n
The denominator is (\u2212254)2(-254)^2(\u2212254)2, so we calculate: (\u2212254)2=64516(-254)^2 = 64516(\u2212254)2=64516<\/p>\n\n\n\n
Thus, the first term becomes: 2+564516\\frac{2 + \\sqrt{5}}{64516}645162+5\u200b\u200b<\/p>\n\n\n\n
Step 3: Simplify the second term inside the parentheses<\/h3>\n\n\n\n
The second term is (2\u22125+2+5)2(2 – 5 + 2 + 5)^2(2\u22125+2+5)2. Let’s first simplify inside the parentheses: 2\u22125+2+5=42 – 5 + 2 + 5 = 42\u22125+2+5=4<\/p>\n\n\n\n
Now, square the result: 42=164^2 = 1642=16<\/p>\n\n\n\n
Thus, the second term becomes: 161616<\/p>\n\n\n\n
Step 4: Combine the two terms<\/h3>\n\n\n\n
Now, the expression becomes: 2+564516\u221216\\frac{2 + \\sqrt{5}}{64516} – 16645162+5\u200b\u200b\u221216<\/p>\n\n\n\n
At this point, we can compute a decimal approximation for the first term. We know that 5\u22482.236\\sqrt{5} \\approx 2.2365\u200b\u22482.236, so: 2+5\u22482+2.236=4.2362 + \\sqrt{5} \\approx 2 + 2.236 = 4.2362+5\u200b\u22482+2.236=4.236<\/p>\n\n\n\n
Now, divide by 64516: 4.23664516\u22486.57\u00d710\u22125\\frac{4.236}{64516} \\approx 6.57 \\times 10^{-5}645164.236\u200b\u22486.57\u00d710\u22125<\/p>\n\n\n\n
So, the expression becomes: 6.57\u00d710\u22125\u2212166.57 \\times 10^{-5} – 166.57\u00d710\u22125\u221216<\/p>\n\n\n\n
Now, subtract: 6.57\u00d710\u22125\u221216\u2248\u221215.99993436.57 \\times 10^{-5} – 16 \\approx -15.99993436.57\u00d710\u22125\u221216\u2248\u221215.9999343<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
\u221215.9999343-15.9999343\u221215.9999343<\/p>\n\n\n\n
This is the approximate value of the expression. Since the first term is so small compared to the second term, it has almost no effect on the final result.<\/p>\n\n\n\n 2 + root 5 by minus 254 squared minus 2 minus 5 + 2 + 5 whole square The Correct Answer and Explanation is: Let’s break down the given expression step by step: The expression is: 2+5(\u2212254)2\u2212(2\u22125+2+5)2\\frac{2 + \\sqrt{5}}{(-254)^2} – (2 – 5 + 2 + 5)^2(\u2212254)22+5\u200b\u200b\u2212(2\u22125+2+5)2 Step 1: Simplify the numerator in the first […]<\/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-258931","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258931","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=258931"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258931\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258931"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258931"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258931"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner9-270.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"