Is 1.875 rational or irrational? Explain Identify the number as rational or irrational square root of 112<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n Correct Answers:<\/strong><\/p>\n\n\n\n Explanation:<\/strong><\/p>\n\n\n\n A rational number<\/strong> is any number that can be written as a fraction or a ratio of two integers, where the denominator is not zero. Rational numbers include integers, fractions, and decimals that terminate or repeat.<\/p>\n\n\n\n The number 1.875 is rational<\/strong> because it is a terminating decimal. It can be written as a fraction: On the other hand, an irrational number<\/strong> is a number that cannot be written as a simple fraction. Its decimal representation is non-terminating and non-repeating. Common examples include \u03c0 (pi) and non-perfect square roots like \u221a2 or \u221a7.<\/p>\n\n\n\n The square root of 112 is irrational<\/strong>. To determine this, look at whether 112 is a perfect square. The perfect squares closest to 112 are 100 (which is 10\u00b2) and 121 (which is 11\u00b2). Since 112 is not a perfect square and cannot be simplified into the square root of a perfect square, \u221a112 is irrational.<\/p>\n\n\n\n For confirmation, we can try to simplify \u221a112:<\/p>\n\n\n\n In summary, 1.875 is rational<\/strong> because it can be written as a fraction (15\/8), and \u221a112 is irrational<\/strong> because it cannot be expressed as a simple fraction and contains the square root of a non-perfect square.<\/p>\n","protected":false},"excerpt":{"rendered":" Is 1.875 rational or irrational? Explain Identify the number as rational or irrational square root of 112 The correct answer and explanation is: Correct Answers: Explanation: A rational number is any number that can be written as a fraction or a ratio of two integers, where the denominator is not zero. Rational numbers include integers, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-40759","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40759","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=40759"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40759\/revisions"}],"predecessor-version":[{"id":40760,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40759\/revisions\/40760"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=40759"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=40759"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=40759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
1.875 = 1875\/1000 = 15\/8 (after simplifying).
Since both 15 and 8 are integers, and 8 is not zero, this confirms 1.875 is a rational number.<\/p>\n\n\n\n\n
Now \u221a7 is a well-known irrational number, and multiplying it by 4 still results in an irrational number. Therefore, \u221a112 = 4\u221a7 is irrational.<\/li>\n<\/ul>\n\n\n\n