Question

to find out the square root of a number by prime factorization

Answer 1

To find the square root of a perfect square by using the prime factorization method when a given number is a perfect square:

Step I: Resolve the given number into prime factors. 

Step II: Make pairs of similar factors. 

Step III: Take the product of prime factors, choosing one factor out of every pair.

Answer 2

I'll explain with ans example:

-Let's take root(16).

When we prime factorize 16 we get root(2x2x2x2) = root(16)

We pair every same numbers and take one of them and remove the root symbol:

root(2x2x2x2)= 2x2 = 4 .

root(16) = 4