{"id":23664,"date":"2025-06-17T20:28:54","date_gmt":"2025-06-17T20:28:54","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=23664"},"modified":"2025-06-17T20:28:58","modified_gmt":"2025-06-17T20:28:58","slug":"which-expression-is-equivalent-to-sqrt-200","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-expression-is-equivalent-to-sqrt-200\/","title":{"rendered":"Which expression is equivalent to sqrt 200"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Which expression is equivalent to sqrt 200<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><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 class=\"wp-block-paragraph\">The expression equivalent to <strong>\u221a200<\/strong> is:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>10\u221a2<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Correct Answer:<\/strong> <strong>10\u221a2<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\udde0 <strong>Explanation (Approx. 300 Words)<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">To simplify the square root of 200, we need to <strong>factor 200 into a product of perfect squares and other factors<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Start by finding the <strong>prime factorization of 200<\/strong>: 200=2\u00d7100=2\u00d7102=2\u00d7(2\u00d75)2200 = 2 \\times 100 = 2 \\times 10^2 = 2 \\times (2 \\times 5)^2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Alternatively: 200=2\u00d7100=2\u00d7(10)2=2\u00d7100200 = 2 \\times 100 = 2 \\times (10)^2 = 2 \\times 100<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, we can break it up: 200=100\u00d72\\sqrt{200} = \\sqrt{100 \\times 2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using the property of square roots: a\u00d7b=a\u00d7b\\sqrt{a \\times b} = \\sqrt{a} \\times \\sqrt{b}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Apply this to our case: 200=100\u00d72=102\\sqrt{200} = \\sqrt{100} \\times \\sqrt{2} = 10\\sqrt{2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is the <strong>simplest radical form<\/strong> of \u221a200.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd0d Why is this useful?<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Simplified form:<\/strong> Mathematicians prefer expressions in their <strong>simplest radical form<\/strong>, as they are easier to use in algebraic equations or comparisons.<\/li>\n\n\n\n<li><strong>Computation:<\/strong> If needed, we can approximate \u221a2 \u2248 1.414. So:<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">10\u00d72\u224810\u00d71.414=14.1410 \\times \\sqrt{2} \\approx 10 \\times 1.414 = 14.14<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This matches the decimal value of \u221a200, which confirms the simplification is correct.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcdd Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Factor 200 = 100 \u00d7 2<\/li>\n\n\n\n<li>\u221a200 = \u221a100 \u00d7 \u221a2 = 10\u221a2<\/li>\n\n\n\n<li>Final answer: <strong>10\u221a2<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This process shows how recognizing perfect square factors helps simplify radicals.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which expression is equivalent to sqrt 200 The correct answer and explanation is: The expression equivalent to \u221a200 is: 10\u221a2 \u2705 Correct Answer: 10\u221a2 \ud83e\udde0 Explanation (Approx. 300 Words) To simplify the square root of 200, we need to factor 200 into a product of perfect squares and other factors. Start by finding the prime [&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-23664","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23664","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=23664"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23664\/revisions"}],"predecessor-version":[{"id":23665,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23664\/revisions\/23665"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=23664"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=23664"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=23664"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}