Correct Answer:<\/h3>\n\n\n\n
200=102\\sqrt{200} = 10\\sqrt{2}200\u200b=102\u200b<\/p>\n\n\n\n
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Step-by-step Explanation:<\/h3>\n\n\n\n
To simplify the square root of 200, you need to look for perfect square factors of 200. A perfect square is a number like 4, 9, 16, 25, 36, and so on. These numbers have whole numbers as their square roots.<\/p>\n\n\n\n
Start by factoring 200:200=2\u00d7100200 = 2 \\times 100200=2\u00d7100<\/p>\n\n\n\n
Now check if 100 is a perfect square. Yes, it is, since:100=10\\sqrt{100} = 10100\u200b=10<\/p>\n\n\n\n
So:200=100\u00d72\\sqrt{200} = \\sqrt{100 \\times 2}200\u200b=100\u00d72\u200b<\/p>\n\n\n\n
Using the property of square roots:a\u00d7b=a\u00d7b\\sqrt{a \\times b} = \\sqrt{a} \\times \\sqrt{b}a\u00d7b\u200b=a\u200b\u00d7b\u200b<\/p>\n\n\n\n
Apply this property:200=100\u00d72\\sqrt{200} = \\sqrt{100} \\times \\sqrt{2}200\u200b=100\u200b\u00d72\u200b200=10\u00d72\\sqrt{200} = 10 \\times \\sqrt{2}200\u200b=10\u00d72\u200b200=102\\sqrt{200} = 10\\sqrt{2}200\u200b=102\u200b<\/p>\n\n\n\n
This is the simplified form because 2\\sqrt{2}2\u200b is already in simplest radical form. It cannot be simplified further because 2 is a prime number and not a perfect square.<\/p>\n\n\n\n
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Why This Works:<\/h3>\n\n\n\n
Simplifying square roots involves factoring out the largest possible perfect square. The goal is to rewrite the number under the square root as a product where one factor is a perfect square. This makes it possible to take that part out of the square root, leaving the result in its simplest radical form.<\/p>\n\n\n\n
In this example, 100 was the perfect square part of 200, and 2 was left inside the radical. By recognizing this, we arrived at a simplified expression that is easier to work with and often required in algebra and geometry problems.<\/p>\n\n\n\n How do you simplify the square root of 200 The Correct Answer and Explanation is: Correct Answer: 200=102\\sqrt{200} = 10\\sqrt{2}200\u200b=102\u200b Step-by-step Explanation: To simplify the square root of 200, you need to look for perfect square factors of 200. A perfect square is a number like 4, 9, 16, 25, 36, and so on. These […]<\/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-25934","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25934","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=25934"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25934\/revisions"}],"predecessor-version":[{"id":25936,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25934\/revisions\/25936"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25934"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25934"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25934"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-19.jpeg\")
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