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.