Which of the following will result in a rational answer?<\/p>\n\n\n\n
multiplying p by a fraction
adding the square root of a non perfect square to a whole
adding the square root of a perfect square to p
multiplying a fraction by a repeating decimal<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The correct answer is: To determine which of the options results in a rational number<\/strong>, we must first understand what a rational number is.<\/p>\n\n\n\n A rational number<\/strong> is any number that can be expressed as a ratio<\/strong> of two integers (a fraction), such as \u00bd, -3, 0.75 (which is 3\/4), or 5 (which is 5\/1). Rational numbers include:<\/p>\n\n\n\n Let\u2019s evaluate each option:<\/p>\n\n\n\n Assume p<\/em> is a rational number (e.g., an integer or a fraction). So, this will result in a rational number<\/strong>. \u2705<\/p>\n\n\n\n The square root of a non-perfect square (like \u221a2, \u221a5, \u221a10) is irrational<\/strong>, meaning it cannot be written as a ratio of two integers. The square root of a perfect square (like \u221a4 = 2, \u221a9 = 3) is rational. However, between this and the first option, the question asked which will<\/strong> result in a rational number \u2014 and both this and the first one are correct if<\/strong> p<\/em> is rational.<\/p>\n\n\n\n A repeating decimal is rational, and a fraction is rational. While more than one option can lead to rational answers, the most universally reliable and simplest<\/strong> is:<\/p>\n\n\n\n \u2705 Multiplying p<\/em> by a fraction<\/strong> \u2014 always gives a rational result if p<\/em> is rational.<\/p>\n","protected":false},"excerpt":{"rendered":" Which of the following will result in a rational answer? multiplying p by a fractionadding the square root of a non perfect square to a wholeadding the square root of a perfect square to pmultiplying a fraction by a repeating decimal The Correct Answer and Explanation is: The correct answer is:Multiplying p by a fraction […]<\/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-216342","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216342","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=216342"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216342\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=216342"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=216342"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=216342"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Multiplying p<\/em> by a fraction<\/strong><\/p>\n\n\n\n
\n\n\n\nExplanation (300+ words):<\/h3>\n\n\n\n
\n
\n\n\n\n1. Multiplying p<\/em> by a fraction<\/strong><\/h3>\n\n\n\n
When you multiply a rational number by another rational number (a fraction is rational by definition), the result will also be rational.
Example:
If p<\/em> = 6 and the fraction is 2\/3, then:
6 \u00d7 2\/3 = 12\/3 = 4 \u2192 which is a rational number.<\/p>\n\n\n\n
\n\n\n\n2. Adding the square root of a non-perfect square to a whole number<\/strong><\/h3>\n\n\n\n
Adding an irrational number to a whole number (which is rational) results in an irrational number<\/strong>.
Example: 3 + \u221a2 is irrational. \u274c<\/p>\n\n\n\n
\n\n\n\n3. Adding the square root of a perfect square to p<\/em><\/strong><\/h3>\n\n\n\n
If p<\/em> is rational, and we add another rational number to it, the result will be rational.
Example: p<\/em> = \u00bd, \u221a9 = 3 \u2192 \u00bd + 3 = 3.5 \u2192 Rational \u2705
This also results in a rational number.<\/strong><\/p>\n\n\n\n
\n\n\n\n4. Multiplying a fraction by a repeating decimal<\/strong><\/h3>\n\n\n\n
Multiplying two rational numbers yields another rational number.
Example: \u00bd \u00d7 0.333\u2026 = 0.1666\u2026 \u2192 This is also rational. \u2705<\/p>\n\n\n\n
\n\n\n\nFinal Determination:<\/h3>\n\n\n\n