{"id":237364,"date":"2025-06-17T07:40:28","date_gmt":"2025-06-17T07:40:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=237364"},"modified":"2025-06-17T07:40:31","modified_gmt":"2025-06-17T07:40:31","slug":"find-all-the-real-square-roots-of-0-0004","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/17\/find-all-the-real-square-roots-of-0-0004\/","title":{"rendered":"Find all the real square roots of 0.0004."},"content":{"rendered":"\n<p>Find all the real square roots of 0.0004. A. 0.00632 and -0.00632 B. 0.06325 and -0.06325 C. 0.0002 and -0.0002 D. 0.02 and -0.02<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer: D. 0.02 and -0.02<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>To find all the <strong>real square roots<\/strong> of 0.0004, we need to determine which number, when multiplied by itself, equals 0.0004. In mathematical terms, we are solving:x2=0.0004x^2 = 0.0004&#215;2=0.0004<\/p>\n\n\n\n<p>To find xxx, we take the square root of 0.0004. The square root of a number has two real roots when the number is positive: one positive and one negative. So we compute:0.0004=0.02\\sqrt{0.0004} = 0.020.0004\u200b=0.02<\/p>\n\n\n\n<p>Therefore, the two real square roots of 0.0004 are:x=0.02andx=\u22120.02x = 0.02 \\quad \\text{and} \\quad x = -0.02x=0.02andx=\u22120.02<\/p>\n\n\n\n<p>This is because:(0.02)2=0.02\u00d70.02=0.0004(0.02)^2 = 0.02 \\times 0.02 = 0.0004(0.02)2=0.02\u00d70.02=0.0004(\u22120.02)2=(\u22120.02)\u00d7(\u22120.02)=0.0004(-0.02)^2 = (-0.02) \\times (-0.02) = 0.0004(\u22120.02)2=(\u22120.02)\u00d7(\u22120.02)=0.0004<\/p>\n\n\n\n<p>The other answer choices are incorrect for the following reasons:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A. 0.00632 and -0.00632<\/strong>: (0.00632)2\u22480.00003994(too\u00a0small)(0.00632)^2 \\approx 0.00003994 \\quad \\text{(too small)}(0.00632)2\u22480.00003994(too\u00a0small)<\/li>\n\n\n\n<li><strong>B. 0.06325 and -0.06325<\/strong>: (0.06325)2\u22480.004(too\u00a0large)(0.06325)^2 \\approx 0.004 \\quad \\text{(too large)}(0.06325)2\u22480.004(too\u00a0large)<\/li>\n\n\n\n<li><strong>C. 0.0002 and -0.0002<\/strong>: (0.0002)2=0.00000004(much\u00a0too\u00a0small)(0.0002)^2 = 0.00000004 \\quad \\text{(much too small)}(0.0002)2=0.00000004(much\u00a0too\u00a0small)<\/li>\n\n\n\n<li><strong>D. 0.02 and -0.02<\/strong>: (0.02)2=0.0004(correct)(0.02)^2 = 0.0004 \\quad \\text{(correct)}(0.02)2=0.0004(correct)<\/li>\n<\/ul>\n\n\n\n<p>In conclusion, the correct answer is <strong>D<\/strong>, because both 0.02 and -0.02 satisfy the equation x2=0.0004x^2 = 0.0004&#215;2=0.0004, and therefore are the real square roots of 0.0004.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-823.jpeg\" alt=\"\" class=\"wp-image-237365\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find all the real square roots of 0.0004. A. 0.00632 and -0.00632 B. 0.06325 and -0.06325 C. 0.0002 and -0.0002 D. 0.02 and -0.02 The Correct Answer and Explanation is: Correct Answer: D. 0.02 and -0.02 To find all the real square roots of 0.0004, we need to determine which number, when multiplied by itself, [&hellip;]<\/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-237364","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237364","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=237364"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237364\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=237364"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=237364"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=237364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}