Find the smallest number by which 396 must be divided to obtain a perfect square. Also find the square root of the perfect square so obtained.

Given: 396

To find: Here we have to find the smallest number by which 396 must be divided to obtain a perfect square.

Solution:

Prime factorization of 396;

396 = 2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 11

A perfect square has each distinct prime factor occurring an even number of times.

So, you should divide 396 by 11

You will get = 36

The square root of the number obtained will be 6.