A number n is said to be the square root of a number n², where n² is obtainted by multiplying the number n with itself once.

i,e. n²=n×n

The symbol of square root is √

Square root of 4 is 2

i,e.√4=2 ( since 4=2×2)

√9=3, √16=4, √25=5 .....

The number whose square root is a whole number is called as Perfect square.

Generally there are two methods to find the square root of a number.

1.Prime Factorization Method

2.Division Method

(i) Prime Factorization Method

In this method first find the prime factors and then pair them as given below.

Example- Find the square root of 144.

Solution:

144 = 2×2×2×2×3×3

So the square root of 144 i,e.

√144 = 2×2×3 = 12

Example- Find the square root of 11025.

Solution:

11025=3×3×5×5×7×7

So the square root of 11025 is

√11025=3×5×7=105

Example- Find the square root of 19600

Solution:

19600=2×2×2×2×5×5×7×7

So the square root of 19600 is

√19600=2×2×5×7=140

(ii) Division Method

In this method first we make pairs from the right side to left side of the given number and then solve as given below.

Example- Find the square root of 3600.

Solution:

So the square root of 3600 is 60.

Example- Find the square root of 120409.

Solution:

So the square root of 120409 is 347.

Example- Find the square root of 11025.

So the square root of 11025 is 105.

For GK Updates visit: The Infinite Studies