To calculate the square root of a power of 10, such as \u221a(10\u207b\u00b3\u00b9) or \u221a(10\u207b\u00b9\u2075), follow these steps:<\/p>\n\n\n\n
General Rule:<\/h3>\n\n\n\n
The square root of 10 raised to a power is equal to 10 raised to half of that power. 10n=10n\/2\\sqrt{10^n} = 10^{n\/2}10n\u200b=10n\/2<\/p>\n\n\n\n
Example 1: \u221a(10\u207b\u00b3\u00b9)<\/h3>\n\n\n\n
Apply the rule: 10\u221231=10\u221231\/2=10\u221215.5\\sqrt{10^{-31}} = 10^{-31\/2} = 10^{-15.5}10\u221231\u200b=10\u221231\/2=10\u221215.5<\/p>\n\n\n\n
So, the square root of 10\u207b\u00b3\u00b9 is 10\u207b\u00b9\u2075.\u2075.<\/p>\n\n\n\n
Example 2: \u221a(10\u207b\u00b9\u2075)<\/h3>\n\n\n\n
10\u221215=10\u221215\/2=10\u22127.5\\sqrt{10^{-15}} = 10^{-15\/2} = 10^{-7.5}10\u221215\u200b=10\u221215\/2=10\u22127.5<\/p>\n\n\n\n
So, the square root of 10\u207b\u00b9\u2075 is 10\u207b\u2077.\u2075.<\/p>\n\n\n\n
\n\n\n\n
Explanation:<\/h3>\n\n\n\n
When dealing with powers of 10, remember that square roots and exponents are related. Taking the square root of a number is the same as raising that number to the one-half power. So when you have: 10n=(10n)1\/2\\sqrt{10^n} = (10^n)^{1\/2}10n\u200b=(10n)1\/2<\/p>\n\n\n\n
By the laws of exponents, you multiply the exponents: (10n)1\/2=10n\u00d71\/2=10n\/2(10^n)^{1\/2} = 10^{n \\times 1\/2} = 10^{n\/2}(10n)1\/2=10n\u00d71\/2=10n\/2<\/p>\n\n\n\n
This rule works regardless of whether the exponent is positive, negative, or a decimal. In scientific and engineering problems, exponents like 10\u207b\u00b3\u00b9 or 10\u207b\u00b9\u2075 often represent very small values, such as atomic scales or extremely short time intervals. Taking their square root allows scientists to simplify equations or convert between units.<\/p>\n\n\n\n
For example, if a quantity is proportional to 10\u207b\u00b3\u00b9, and a formula involves the square root of that quantity, the answer becomes 10\u207b\u00b9\u2075.\u2075. Knowing this exponent rule saves time and helps avoid the use of a calculator. It is especially useful in logarithmic scales, scientific notation, and exponential equations.<\/p>\n\n\n\n How to Calculate the Square Root of a Power of 10, for Example the Square Root of 10^-31 or 10^-15. The Correct Answer and Explanation is: To calculate the square root of a power of 10, such as \u221a(10\u207b\u00b3\u00b9) or \u221a(10\u207b\u00b9\u2075), follow these steps: General Rule: The square root of 10 raised to a power […]<\/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-27261","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27261","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=27261"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27261\/revisions"}],"predecessor-version":[{"id":27279,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27261\/revisions\/27279"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=27261"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=27261"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=27261"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-154.jpeg\")
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