{"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
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
We will understand this by taking an example. Let 7016 be a given number.<\/p>\n
\n1). 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