{"id":44082,"date":"2025-06-30T13:01:24","date_gmt":"2025-06-30T13:01:24","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=44082"},"modified":"2025-06-30T13:01:25","modified_gmt":"2025-06-30T13:01:25","slug":"square-root-of-12-4-irrational-or-rational-number","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/square-root-of-12-4-irrational-or-rational-number\/","title":{"rendered":"Square root of 12\/4 irrational or rational number"},"content":{"rendered":"\n

Square root of 12\/4 irrational or rational number<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The square root of 124\\frac{12}{4}412\u200b is a rational number<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To determine whether the square root of 124\\frac{12}{4}412\u200b is rational or irrational, we first simplify the expression. The fraction 124\\frac{12}{4}412\u200b simplifies to 3. Therefore, we are looking at the square root of 3:124=3\\sqrt{\\frac{12}{4}} = \\sqrt{3}412\u200b\u200b=3\u200b<\/p>\n\n\n\n

Now, to decide if 3\\sqrt{3}3\u200b is a rational or irrational number, we need to recall the definitions:<\/p>\n\n\n\n

    \n
  • Rational numbers<\/strong> are numbers that can be expressed as a fraction of two integers (i.e., in the form pq\\frac{p}{q}qp\u200b, where ppp and qqq are integers, and q\u22600q \\neq 0q\ue020=0).<\/li>\n\n\n\n
  • Irrational numbers<\/strong> are numbers that cannot be expressed as a fraction of two integers. They have non-repeating and non-terminating decimal expansions.<\/li>\n<\/ul>\n\n\n\n

    Next, we examine 3\\sqrt{3}3\u200b. It is well-known that the square roots of non-perfect squares (like 3, 2, 5, etc.) are irrational numbers. This is because no integer squared equals 3, and there is no fraction pq\\frac{p}{q}qp\u200b that, when squared, equals 3. The decimal representation of 3\\sqrt{3}3\u200b is approximately 1.732050807568877… and it continues without repeating or terminating.<\/p>\n\n\n\n

    Since 3\\sqrt{3}3\u200b cannot be written as a fraction of integers and its decimal representation does not terminate or repeat, it is an irrational number. Therefore, the square root of 124\\frac{12}{4}412\u200b is irrational.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Square root of 12\/4 irrational or rational number The Correct Answer and Explanation is: The square root of 124\\frac{12}{4}412\u200b is a rational number. Explanation: To determine whether the square root of 124\\frac{12}{4}412\u200b is rational or irrational, we first simplify the expression. The fraction 124\\frac{12}{4}412\u200b simplifies to 3. Therefore, we are looking at the square root […]<\/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-44082","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44082","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=44082"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44082\/revisions"}],"predecessor-version":[{"id":44085,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44082\/revisions\/44085"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=44082"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=44082"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=44082"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}