{"id":25929,"date":"2025-06-19T08:11:24","date_gmt":"2025-06-19T08:11:24","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25929"},"modified":"2025-06-19T08:11:26","modified_gmt":"2025-06-19T08:11:26","slug":"go-step-by-step-to-reduce-the-radical","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/go-step-by-step-to-reduce-the-radical\/","title":{"rendered":"Go step by step to reduce the radical."},"content":{"rendered":"\n<p>Go step by step to reduce the radical.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"433\" height=\"162\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-41.png\" alt=\"\" class=\"wp-image-25930\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-41.png 433w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-41-300x112.png 300w\" sizes=\"auto, (max-width: 433px) 100vw, 433px\" \/><\/figure>\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<p>To reduce the radical expression \u221a200 step by step:<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Prime factorize 200<\/strong> Start by breaking 200 into its prime factors: 200 = 2 \u00d7 100 100 = 2 \u00d7 50 50 = 2 \u00d7 25 25 = 5 \u00d7 5 So, 200 = 2 \u00d7 2 \u00d7 2 \u00d7 5 \u00d7 5 = 23\u00d7522^3 \\times 5^2<\/li>\n\n\n\n<li><strong>Apply the square root to the factorization<\/strong> \u221a200 = \u221a(2 \u00d7 2 \u00d7 2 \u00d7 5 \u00d7 5) Rearranged as \u221a(2\u00b2 \u00d7 5\u00b2 \u00d7 2)<\/li>\n\n\n\n<li><strong>Separate into known square roots and remainder<\/strong> \u221a200 = \u221a(2\u00b2) \u00d7 \u221a(5\u00b2) \u00d7 \u221a2 \u221a(2\u00b2) = 2, \u221a(5\u00b2) = 5, and \u221a2 remains<\/li>\n\n\n\n<li><strong>Multiply the constants<\/strong> 2 \u00d7 5 = 10<\/li>\n<\/ol>\n\n\n\n<p><strong>Final simplified answer:<\/strong> <strong>\u221a200 = 10\u221a2<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>When simplifying a radical, the goal is to express the number inside the square root in terms of perfect squares multiplied by any leftover non-square factors. In this case, the number 200 is not a perfect square itself, so we look for factors of 200 that are perfect squares. We start by decomposing 200 into its prime components: three factors of 2 and two factors of 5. From this, we identify that 222^2 and 525^2 are perfect squares.<\/p>\n\n\n\n<p>Using the property that the square root of a product equals the product of the square roots, we separate the perfect squares and pull them out of the radical. Each square root of a perfect square becomes a whole number outside the radical. The leftover 2, which is not part of a square pair, remains under the square root sign.<\/p>\n\n\n\n<p>This simplification process transforms the square root of a composite number into a cleaner expression that\u2019s easier to handle in equations or further algebraic work. The result, 10\u221a2, is fully simplified because \u221a2 is already in its simplest radical form. This method is broadly applicable in both pure and applied mathematics, making radical simplification a key tool in problem solving<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-18.jpeg\" alt=\"\" class=\"wp-image-25931\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-18.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-18-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Go step by step to reduce the radical. The Correct Answer and Explanation is: To reduce the radical expression \u221a200 step by step: Final simplified answer: \u221a200 = 10\u221a2 Explanation: When simplifying a radical, the goal is to express the number inside the square root in terms of perfect squares multiplied by any leftover non-square [&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-25929","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25929","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=25929"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25929\/revisions"}],"predecessor-version":[{"id":25932,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25929\/revisions\/25932"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25929"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25929"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25929"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}