The principal square root<\/strong> of a number refers to the non-negative root of that number. For any positive real number x<\/em>, the square root symbol \u221ax refers specifically to the positive root. Every positive real number has two square roots, one positive and one negative, but by convention, the square root symbol represents only the positive value.<\/p>\n\n\n\n
Example 1: \u221a48<\/h4>\n\n\n\n
The square root of 48 is an irrational number. Using a calculator: \u221a48 \u2248 6.928 This is the positive square root, known as the principal root.<\/p>\n\n\n\n
Example 2: \u221a0.025<\/h4>\n\n\n\n
This is a small decimal number. To compute: \u221a0.025 = \u221a(25\/1000) = \u221a(1\/40) \u2248 0.158 Thus, the principal square root is approximately 0.158.<\/p>\n\n\n\n
Example 3: \u221a0.49<\/h4>\n\n\n\n
Since 0.49 is a perfect square of 0.7: \u221a0.49 = 0.7<\/p>\n\n\n\n
Example 4: \u221a(25\/9)<\/h4>\n\n\n\n
For fractions, take the square root of the numerator and denominator separately: \u221a(25\/9) = \u221a25 \u00f7 \u221a9 = 5 \u00f7 3 = 5\/3 \u2248 1.667<\/p>\n\n\n\n
Example 5: \u221a125<\/h4>\n\n\n\n
125 is not a perfect square, but its square root is simplified as: \u221a125 = \u221a(25 \u00d7 5) = \u221a25 \u00d7 \u221a5 = 5\u221a5 Approximating \u221a5 \u2248 2.236 gives: \u221a125 \u2248 5 \u00d7 2.236 = 11.180<\/p>\n\n\n\n
These calculations emphasize the difference between exact forms (like 5\u221a5) and decimal approximations. When expressing square roots, both forms are valid depending on the situation, but for numerical approximations, decimals are often used. The principal root always refers to the positive value.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
Principal root of square root 48, square root 0.025, square root 0.49, square root 25\/9, and square root 125? The Correct Answer and Explanation is: Correct Answers for Principal Square Roots: Explanation: The principal square root of a number refers to the non-negative root of that number. For any positive real number x, the square […]<\/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-33032","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33032","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=33032"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33032\/revisions"}],"predecessor-version":[{"id":33034,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33032\/revisions\/33034"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=33032"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=33032"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=33032"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
![\"\"](\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-479.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"