{"id":20046,"date":"2025-06-13T23:05:47","date_gmt":"2025-06-13T23:05:47","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=20046"},"modified":"2025-06-13T23:05:48","modified_gmt":"2025-06-13T23:05:48","slug":"find-the-square-root-of-7-3-upto-3-decimal-places","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-square-root-of-7-3-upto-3-decimal-places\/","title":{"rendered":"Find the square root of 7.3 upto 3 decimal places"},"content":{"rendered":"\n<p>Find the square root of 7.3 upto 3 decimal places.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><br>The square root of 7.3 up to three decimal places is <strong>2.702<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation (300 words):<\/strong><br>Finding the square root of a number involves determining a value that, when multiplied by itself, gives the original number. In this case, we are looking for the square root of <strong>7.3<\/strong>, which is not a perfect square. This means its square root will be an <strong>irrational number<\/strong>\u2014a non-repeating, non-terminating decimal.<\/p>\n\n\n\n<p>To find the square root up to three decimal places, we can use several methods:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Estimation and successive approximation<\/li>\n\n\n\n<li>Long division method<\/li>\n\n\n\n<li>A calculator (for speed and precision)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Using a Calculator:<\/h3>\n\n\n\n<p>The quickest and most accurate method is using a scientific calculator or a programming tool. Inputting \u221a7.3 gives: 7.3\u22482.7018512&#8230;\\sqrt{7.3} \u2248 2.7018512&#8230;<\/p>\n\n\n\n<p>When rounding to <strong>three decimal places<\/strong>, we look at the fourth digit after the decimal:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The first three digits: <strong>2.701<\/strong><\/li>\n\n\n\n<li>The next digit is <strong>8<\/strong>, which is greater than 5, so we <strong>round up<\/strong> the last digit<\/li>\n<\/ul>\n\n\n\n<p>Thus: 7.3\u22482.702\\sqrt{7.3} \u2248 \\boxed{2.702}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Using Estimation:<\/h3>\n\n\n\n<p>We know:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u221a4 = 2<\/li>\n\n\n\n<li>\u221a9 = 3<br>So \u221a7.3 lies between 2 and 3.<\/li>\n<\/ul>\n\n\n\n<p>Try:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2.7\u00b2 = 7.29<\/li>\n\n\n\n<li>2.71\u00b2 = 7.3441 (too high)<\/li>\n\n\n\n<li>So the value must be between 2.7 and 2.71<\/li>\n<\/ul>\n\n\n\n<p>Refining further:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2.705\u00b2 = 7.316025<\/li>\n\n\n\n<li>2.702\u00b2 = 7.304804 (very close to 7.3)<\/li>\n<\/ul>\n\n\n\n<p>So by iterating this way, we also arrive at <strong>2.702<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The square root of 7.3, accurate to three decimal places, is <strong>2.702<\/strong>. This level of precision is often sufficient in science, engineering, and finance unless extremely high accuracy is needed.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the square root of 7.3 upto 3 decimal places. The correct answer and explanation is: Correct Answer:The square root of 7.3 up to three decimal places is 2.702. Explanation (300 words):Finding the square root of a number involves determining a value that, when multiplied by itself, gives the original number. In this case, we [&hellip;]<\/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-20046","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20046","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=20046"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20046\/revisions"}],"predecessor-version":[{"id":20047,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20046\/revisions\/20047"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=20046"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=20046"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=20046"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}