Correct Answer:<\/h3>\n\n\n\n
The square root of 125 in simplest form is125=55\\sqrt{125} = 5\\sqrt{5}125\u200b=55\u200b<\/p>\n\n\n\n
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Explanation:<\/h3>\n\n\n\n
To simplify the square root of 125, begin by finding its prime factorization. The number 125 is not a perfect square, but it can be broken down into smaller factors:<\/p>\n\n\n\n
125 = 5 \u00d7 25
Then break 25 further: 25 = 5 \u00d7 5
So, 125 = 5 \u00d7 5 \u00d7 5 = 535^353<\/p>\n\n\n\n
Now apply the square root to this factorization:125=5\u00d75\u00d75\\sqrt{125} = \\sqrt{5 \\times 5 \\times 5}125\u200b=5\u00d75\u00d75\u200b<\/p>\n\n\n\n
Group the pairs of the same factor. In this case, we have two fives that can form a perfect square:125=52\u00d75\\sqrt{125} = \\sqrt{5^2 \\times 5}125\u200b=52\u00d75\u200b<\/p>\n\n\n\n
Using the square root property a\u00d7b=a\u00d7b\\sqrt{a \\times b} = \\sqrt{a} \\times \\sqrt{b}a\u00d7b\u200b=a\u200b\u00d7b\u200b, split the expression:125=52\u00d75\\sqrt{125} = \\sqrt{5^2} \\times \\sqrt{5}125\u200b=52\u200b\u00d75\u200b<\/p>\n\n\n\n
Now simplify the square root of the perfect square 52=5\\sqrt{5^2} = 552\u200b=5:125=55\\sqrt{125} = 5 \\sqrt{5}125\u200b=55\u200b<\/p>\n\n\n\n
So the simplest form of 125\\sqrt{125}125\u200b is 555 \\sqrt{5}55\u200b.<\/p>\n\n\n\n
This simplified form is useful in mathematics, especially in algebra, geometry, and trigonometry, where you are often required to express radicals in their simplest form. Simplifying radicals helps make calculations easier, reduces the risk of error, and reveals more meaningful relationships between numbers. Although 125 is not a perfect square, part of it (25) is. Recognizing and extracting perfect squares allows us to rewrite square roots in terms of whole numbers and simpler irrational parts.<\/p>\n\n\n\n
In decimal form, 125\u224811.18\\sqrt{125} \\approx 11.18125\u200b\u224811.18, but 555 \\sqrt{5}55\u200b is the exact and simplified radical expression.<\/p>\n\n\n\n What is the square root of 125 in simplest forms The Correct Answer and Explanation is: Correct Answer: The square root of 125 in simplest form is125=55\\sqrt{125} = 5\\sqrt{5}125\u200b=55\u200b Explanation: To simplify the square root of 125, begin by finding its prime factorization. The number 125 is not a perfect square, but it can be […]<\/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-25511","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25511","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=25511"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25511\/revisions"}],"predecessor-version":[{"id":25513,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25511\/revisions\/25513"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25511"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25511"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-44.jpeg\")
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