# CLASS-8FINDING SQUARE ROOT BY PRIME FACTORIZATION METHOD

Finding Square Root By Prime Factorization

Step.1) We have to write the number as a product of prime factors.

Step.2)  Make pairs of equal prime factors

Step.3) Take one factor from each pair and multiply them.

We can also express the number as a product of powers of prime factors, taking half of each index and then finding the product of the factors will give the square root

There are some example are given below for better understanding –

1)  Find the square root of 5625

So, 5625  =  5 X 5 X 5 X 5 X 3 X 3

= ( 5 X 5 ) X ( 5 X 5 ) X ( 3 X 3 )

√5625  =  5 X 5 X 3  =  75

On the other way –

5625 = 5⁴ X 3²

So, √5625 = 5² X 3 = 25 X 3 = 75

2) Find the square root of 19600

So, 19600 =  5 X 5 X 4 X 4 X 7 X 7

= ( 5 X 5 ) X ( 4 X 4 ) X ( 7 X 7 )

√19600 = 5 X 4 X 7 = 140

On the other way –

19600 = 5² X 4² X 7²

So, √19600 = 5 X 4 X 7 = 140

3) Find the square root of 48400

So, 48400 = 5 X 5 X 4 X 4 X 11 X 11

= ( 5 X 5 ) X ( 4 X 4 ) X ( 11 X 11 )

√48400 = 5 X 4 X 11 = 220

On the other way –

48400 = 5² X 4² X 11²

So, √48400 = 5 X 4 X 11 = 220