{"id":34625,"date":"2025-06-23T17:23:01","date_gmt":"2025-06-23T17:23:01","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=34625"},"modified":"2025-06-23T17:23:02","modified_gmt":"2025-06-23T17:23:02","slug":"simplify-the-square-root-of-7-over-18","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/simplify-the-square-root-of-7-over-18\/","title":{"rendered":"simplify the square root of 7 over 18"},"content":{"rendered":"\n
simplify the square root of 7 over 18<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
To simplify the expression 718\\sqrt{\\frac{7}{18}}187\u200b\u200b, follow these steps:<\/p>\n\n\n\n
Step 1: Apply the property of square roots to a fraction<\/strong><\/h3>\n\n\n\n
Step 2: Simplify the denominator 18\\sqrt{18}18\u200b<\/strong><\/h3>\n\n\n\n
18 is not a perfect square, but it can be factored as 9\u00d729 \\times 29\u00d72. Since 9 is a perfect square:18=9\u22c52=9\u22c52=32\\sqrt{18} = \\sqrt{9 \\cdot 2} = \\sqrt{9} \\cdot \\sqrt{2} = 3\\sqrt{2}18\u200b=9\u22c52\u200b=9\u200b\u22c52\u200b=32\u200b<\/p>\n\n\n\n
Step 3: Substitute back into the expression<\/strong><\/h3>\n\n\n\n
Step 4: Rationalize the denominator<\/strong><\/h3>\n\n\n\n
To eliminate the square root from the denominator, multiply both the numerator and denominator by 2\\sqrt{2}2\u200b:732\u22c522=143\u22c52=146\\frac{\\sqrt{7}}{3\\sqrt{2}} \\cdot \\frac{\\sqrt{2}}{\\sqrt{2}} = \\frac{\\sqrt{14}}{3 \\cdot 2} = \\frac{\\sqrt{14}}{6}32\u200b7\u200b\u200b\u22c52\u200b2\u200b\u200b=3\u22c5214\u200b\u200b=614\u200b\u200b<\/p>\n\n\n\n
Simplifying square roots involving fractions follows a specific process based on the properties of radicals. In this case, we begin with the square root of the fraction 718\\frac{7}{18}187\u200b. The square root of a fraction can be split into the square root of the numerator over the square root of the denominator, which gives 718\\frac{\\sqrt{7}}{\\sqrt{18}}18\u200b7\u200b\u200b.<\/p>\n\n\n\n
The next step is to simplify the denominator. Although 18 is not a perfect square, it can be factored into 9 times 2. Since 9 is a perfect square, its square root is 3. This means 18=32\\sqrt{18} = 3\\sqrt{2}18\u200b=32\u200b. Substituting this simplified form into the expression gives 732\\frac{\\sqrt{7}}{3\\sqrt{2}}32\u200b7\u200b\u200b.<\/p>\n\n\n\n
At this stage, the denominator still contains a radical, which is generally not preferred in final mathematical answers. To resolve this, we use a process called rationalizing the denominator. This involves multiplying the entire expression by a form of 1 that will eliminate the radical in the denominator. In this case, we multiply by 22\\frac{\\sqrt{2}}{\\sqrt{2}}2\u200b2\u200b\u200b, which is equal to 1 and does not change the value of the expression. The result becomes 146\\frac{\\sqrt{14}}{6}614\u200b\u200b, since 7\u22c52=14\\sqrt{7} \\cdot \\sqrt{2} = \\sqrt{14}7\u200b\u22c52\u200b=14\u200b, and 32\u22c52=3\u22c52=63\\sqrt{2} \\cdot \\sqrt{2} = 3 \\cdot 2 = 632\u200b\u22c52\u200b=3\u22c52=6.<\/p>\n\n\n\n
The final expression, 146\\frac{\\sqrt{14}}{6}614\u200b\u200b, is simplified and rationalized. This result cannot be simplified further since 14 is not a perfect square and the square root of 14 cannot be expressed in simpler radical form.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
simplify the square root of 7 over 18 The Correct Answer and Explanation is: To simplify the expression 718\\sqrt{\\frac{7}{18}}187\u200b\u200b, follow these steps: Step 1: Apply the property of square roots to a fraction 718=718\\sqrt{\\frac{7}{18}} = \\frac{\\sqrt{7}}{\\sqrt{18}}187\u200b\u200b=18\u200b7\u200b\u200b Step 2: Simplify the denominator 18\\sqrt{18}18\u200b 18 is not a perfect square, but it can be factored as 9\u00d729 […]<\/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-34625","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34625","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=34625"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34625\/revisions"}],"predecessor-version":[{"id":34637,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34625\/revisions\/34637"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=34625"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=34625"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=34625"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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