Question

Find the smallest number by which 396 must be multiplied so that the product becomes a perfect square

Answer 1

396 = 2×2×3×3×11.
11 is not in pair so if we multiplied the given number by 11 it will be a perfect square

Answer 2

Answer:

The very first step to the solution of this problem is to calculate the L.C.M of the number 396 to achieve its prime factors.

L.C.M of the number 396 is;

396 = 2*2*3*3*11

To make 396 a perfect square, we've to multiply 396 with 11 because 2 & 3 are in pairs and 11 is the only unpaired number.

396*11 = 2*2*3*3*11*11

4356 = 2*2*3*3*11*11

Taking square root of 4356 will give us 66 which is equal to 2*3*11.

So the smallest number by which 396 is multiplied to get its perfect square is 11.