{"id":7557,"date":"2021-10-26T17:44:38","date_gmt":"2021-10-26T12:14:38","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7557"},"modified":"2021-11-27T17:36:56","modified_gmt":"2021-11-27T12:06:56","slug":"how-to-find-square-root-and-cube-root-of-number","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/how-to-find-square-root-and-cube-root-of-number\/","title":{"rendered":"How to Find Square Root and Cube Root of Number"},"content":{"rendered":"

Here you will learn how to find square root and cube root of a number and properties of squares and cubes.<\/p>\n

Let’s begin –<\/p>\n

Square Root and Cube Root<\/h2>\n

(a) Square and Square Roots<\/h3>\n

When any number multiplied by itself, it is called as the square of the number.<\/p>\n

Thus, 3 \\(\\times\\) 3 = \\(3^2\\) = 9<\/p>\n

How to find square root of a given number<\/strong><\/h4>\n

We will understand this by taking an example. Let 7016 be a given number.<\/p>\n

\n

1). Write down the number 7016 as a product of its prime factors,<\/p>\n

7016 = \\(2 \\times 2 \\times 2 \\times 2 \\times 21 \\times 21\\)<\/p>\n

= \\(2^4\\times 21^2\\)<\/p>\n

2). The required square root is obtained by having the values of the powers.<\/p>\n

Hence. \\(sqrt{7016}\\) = \\(2^2\\times 21^1\\) = 84<\/p>\n<\/blockquote>\n

Properties of Squares<\/strong><\/h4>\n

1). When a perfect square is written as a product of its prime factors each prime factor will appear an even number of times.<\/p>\n

2). The difference between the square of two consecutive natural numbers is always equal to the sum of the natural numbers. Thus, \\(41^2\\) – \\(40^2\\) = (40 + 41) = 81<\/p>\n

3). The square of a number ending in 1, 5 or 6 also ends in 1, 5 or 6 respectively.<\/p>\n

4). The square of any number ending in 5 : The last two digits will always be 25.<\/p>\n

5). The square of any number is always non-negative.<\/p>\n

Cubes and Cube Roots<\/h3>\n

When a number s multiplied with itself two times, we get the cube of the number.<\/p>\n

Thus, \\(x \\times x \\times x\\) = \\(x^3\\)<\/p>\n

How to find cube root of a given number<\/strong><\/h4>\n

In order to find the cube root of a number, first we write it in its standard form and divide all powers by 3.<\/p>\n

Thus, the cube root of \\(3^6 \\times 5^9 \\times 17^3 \\times 2^6\\) is given by<\/p>\n

\\(3^2 \\times 5^3 \\times 17^ \\times 2^2\\)<\/p>\n

Properties of Cubes<\/strong><\/h4>\n

1). When a perfect cube is written in its standard form the values of the powers on each prime factor will be a multiple of 3.<\/p>\n

2). The cubes of all numbers (integers and decimals) greater than 1 are greater than the number itself.<\/p>\n

3). The value of the cubes of a number between 0 and 1 is lower than the number itself.<\/p>\n

4). The cube of a number between 0 and -1 is greater than the number itself.<\/p>\n

5). The cube of any number less than -1, is always lower than the number.<\/p>\n\n\n

\n
Next – What are Prime Numbers in Math<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Concepts of Number System<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn how to find square root and cube root of a number and properties of squares and cubes. Let’s begin – Square Root and Cube Root (a) Square and Square Roots When any number multiplied by itself, it is called as the square of the number. Thus, 3 \\(\\times\\) 3 = \\(3^2\\) …<\/p>\n

How to Find Square Root and Cube Root of Number<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[62],"tags":[511,509,510],"yoast_head":"\nHow to Find Square Root and Cube Root of Number - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn how to find square root and cube root of a number and properties of squares and cubes.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/how-to-find-square-root-and-cube-root-of-number\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to Find Square Root and Cube Root of Number - 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