Question

In this case, if we want to find the smallest factor with which we can multiply or divide 108 to get a square number, what should we do?

Answer 1

108 = 2 × 2 × 3 × 3 × 3 = 2² × 3² × 3

If we multiply the factors by 3, then we get
2² × 3² × 3 × 3 ⇒ 2² × 3² × 3² = (2 × 3 × 3)²

Which is a perfect square.

∴ Again if we divide by 3 then we get 2² × 3² ⇒ (2 × 3 )², a perfect square.

∴ We have to multiply or divide 108 by 3 to get a perfect square.