Square Root


The square root of a number is that number which when multiplied by itself gives the given number. It is denoted by the symbol .

What is the square root of a number x?

The square root of a number x is that number which when multiplied by itself gives x as the product. We denote the square root of a number x by √x. 



For example:

(i) 1² = 1

Therefore, square root of 1 is 1. Symbolically √1 = 1.

(ii) 2² = 4

Therefore, square root of 4 is 2. Symbolically √4 = 2.

(iii) 3² = 9

Therefore, square root of 9 is 3. Symbolically √9 = 3.

(iv) 5 is the square root of 25. Since 5² = 25

Or we can write it as √25 = 5 (Square root of 25 is 5)

(v) ²/₃ is the square root of ⁴/₉. Since 2²/3² = ⁴/₉

Or we can write it as √(⁴/₉) = ²/₃ (Square root of ⁴/₉ is ²/₃)

(vi) 0.2 is the square root of 0.04. Since 0.2² = 0.04

Or we can write it as √0.04 = 0.2 (Square root of 0.04 is 0.2)

In general; if n = m², then m is the square root of n, i.e., m = √n

Then in square root we will learn about; square root of a perfect square by using the prime factorization method and square root of a perfect square by using the long division method.


 Square Root

Square Root

Square Root of a Perfect Square by using the Prime Factorization Method

Square Root of a Perfect Square by Using the Long Division Method

Square Root of Numbers in the Decimal Form

Square Root of Number in the Fraction Form

Square Root of Numbers that are Not Perfect Squares

Table of Square Roots

Practice Test on Square and Square Roots


● Square Root- Worksheets

Worksheet on Square Root using Prime Factorization Method

Worksheet on Square Root using Long Division Method

Worksheet on Square Root of Numbers in Decimal and Fraction Form













8th Grade Math Practice

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