Question

Find the smallest number by which 180 must be multiplied so that it becames a perfect square. Also, find the square root of the perfect square so obtained.

Answer 1

180 = 2² × 3² × 5 

= (2 × 2) × (3 × 3) × 5 

To make the unpaired 5 into paired, multiply the number with 5 Therefore, 

180 × 5 = 2² × 3² × 5²

Hence, square root of number = \(\sqrt{180}\) x \(\sqrt{5}\) = 2 x 3 x 5

= 30