{"id":25422,"date":"2025-06-19T02:32:05","date_gmt":"2025-06-19T02:32:05","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25422"},"modified":"2025-06-19T02:32:06","modified_gmt":"2025-06-19T02:32:06","slug":"estimate-the-cube-root-of-the-following-numbers-up-to-one-decimal-place","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/estimate-the-cube-root-of-the-following-numbers-up-to-one-decimal-place\/","title":{"rendered":"Estimate the cube root of the following numbers up to one decimal place"},"content":{"rendered":"\n<p>Estimate the cube root of the following numbers up to one decimal place. (i) 345 (ii) 1275 (iii) 8998<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Estimated Cube Roots (to one decimal place):<\/h3>\n\n\n\n<p>(i) \u221b345 \u2248 <strong>7.0<\/strong><br>(ii) \u221b1275 \u2248 <strong>10.9<\/strong><br>(iii) \u221b8998 \u2248 <strong>20.8<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To estimate the cube root of a number up to one decimal place, we identify two perfect cubes between which the number lies, then use trial and error or interpolation to narrow down the decimal.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">(i) \u221b345<\/h4>\n\n\n\n<p>We know:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u221b216 = 6 (because 6\u00b3 = 216)<\/li>\n\n\n\n<li>\u221b343 = 7 (because 7\u00b3 = 343)<\/li>\n\n\n\n<li>\u221b512 = 8 (because 8\u00b3 = 512)<\/li>\n<\/ul>\n\n\n\n<p>Since 345 is just above 343, its cube root will be a bit more than 7. Trying 7.0:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>7.0\u00b3 = 343<br>Trying 7.1:<\/li>\n\n\n\n<li>7.1\u00b3 = 357.911<br>So, \u221b345 is slightly more than 7.0 but less than 7.1. Since 345 is very close to 343, we round down:<\/li>\n\n\n\n<li><strong>\u221b345 \u2248 7.0<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">(ii) \u221b1275<\/h4>\n\n\n\n<p>We know:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u221b1000 = 10 (10\u00b3 = 1000)<\/li>\n\n\n\n<li>\u221b1331 = 11 (11\u00b3 = 1331)<br>So, 1275 lies between 1000 and 1331. Try 10.8:<\/li>\n\n\n\n<li>10.8\u00b3 = 1259.712<br>Try 10.9:<\/li>\n\n\n\n<li>10.9\u00b3 = 1295.029<\/li>\n<\/ul>\n\n\n\n<p>1275 lies between these two values, but closer to 10.8.9, so we choose:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u221b1275 \u2248 10.9<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">(iii) \u221b8998<\/h4>\n\n\n\n<p>We know:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u221b8000 = 20 (20\u00b3 = 8000)<\/li>\n\n\n\n<li>\u221b9261 = 21 (21\u00b3 = 9261)<br>So, 8998 is between 8000 and 9261. Try 20.8:<\/li>\n\n\n\n<li>20.8\u00b3 = 8991.872<br>Try 20.9:<\/li>\n\n\n\n<li>20.9\u00b3 = 9125.129<\/li>\n<\/ul>\n\n\n\n<p>Since 8998 is closer to 8991.872, we choose:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u221b8998 \u2248 20.8<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<p>Estimation uses perfect cubes as reference points and checks nearby decimals. We approximate by testing numbers just above or below the boundaries. This method helps when a calculator is not available and reinforces number sense.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-21.jpeg\" alt=\"\" class=\"wp-image-25423\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-21.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-21-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-21-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-21-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Estimate the cube root of the following numbers up to one decimal place. (i) 345 (ii) 1275 (iii) 8998 The Correct Answer and Explanation is: Estimated Cube Roots (to one decimal place): (i) \u221b345 \u2248 7.0(ii) \u221b1275 \u2248 10.9(iii) \u221b8998 \u2248 20.8 Explanation: To estimate the cube root of a number up to one decimal [&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-25422","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25422","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=25422"}],"version-history":[{"count":2,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25422\/revisions"}],"predecessor-version":[{"id":25425,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25422\/revisions\/25425"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25422"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25422"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25422"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}