Question

Find the smallest number by which 252 must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained.

Answer 1

Resolving 252 into prime factors, we get 

252 = 2 × 2 × 3 × 3 × 7 

Thus, the 253 must be multiplied by 7 in order to get a perfect square 

Therefore, 

New number = 252 × 7 = 1764 

Hence,

\(\sqrt{1764}\) = 2 × 3 × 7

= 42