Classify the following number as rational or irrational <\/p>\n\n\n\n
(a) root 15 (b) root 625 (c) 2.662 (d) 0.1501500150001500001\u2026\u2026<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n Let’s classify each of the numbers as either rational<\/strong> or irrational<\/strong>:<\/p>\n\n\n\n The number ( \\sqrt{15} ) is irrational<\/strong>. A number is considered irrational if it cannot be expressed as a fraction of two integers. The square root of 15 is a non-repeating, non-terminating decimal. Since 15 is not a perfect square, ( \\sqrt{15} ) does not result in a whole number, and its decimal expansion is infinite without repeating. Therefore, ( \\sqrt{15} ) is irrational.<\/p>\n\n\n\n The number ( \\sqrt{625} ) is rational<\/strong>. ( \\sqrt{625} ) equals 25, which is an integer. An integer is always a rational number because it can be expressed as a fraction, with the integer as the numerator and 1 as the denominator (for example, ( 25 = \\frac{25}{1} )). Thus, ( \\sqrt{625} = 25 ) is a rational number.<\/p>\n\n\n\n The number 2.662 is rational<\/strong>. A rational number is any number that can be expressed as a fraction of two integers, including terminating decimals. The decimal 2.662 is a terminating decimal, and it can be written as the fraction ( \\frac{2662}{1000} ). Since it is a terminating decimal, 2.662 is a rational number.<\/p>\n\n\n\n The number ( 0.1501500150001500001\\ldots ) is rational<\/strong>. This number has a repeating pattern of digits: “150”, which repeats indefinitely. A number with a repeating decimal is always rational, because it can be expressed as a fraction. Specifically, repeating decimals can be converted into fractions using algebraic techniques. In this case, the repeating sequence is “150”, which makes it a rational number.<\/p>\n\n\n\n Explanation of Rational and Irrational Numbers:<\/strong><\/p>\n\n\n\n Thus, by examining the properties of each number, we can confidently classify them as either rational or irrational.<\/p>\n","protected":false},"excerpt":{"rendered":" Classify the following number as rational or irrational (a) root 15 (b) root 625 (c) 2.662 (d) 0.1501500150001500001\u2026\u2026 The Correct Answer and Explanation is: Let’s classify each of the numbers as either rational or irrational: (a) ( \\sqrt{15} ) The number ( \\sqrt{15} ) is irrational. A number is considered irrational if it cannot be […]<\/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-169282","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/169282","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=169282"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/169282\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=169282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=169282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=169282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}(a) ( \\sqrt{15} )<\/h3>\n\n\n\n
(b) ( \\sqrt{625} )<\/h3>\n\n\n\n
(c) 2.662<\/h3>\n\n\n\n
(d) ( 0.1501500150001500001\\ldots )<\/h3>\n\n\n\n
Summary:<\/h3>\n\n\n\n
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