Question

Find the smallest number by which 2400 is to be multiplied to get a perfect square and also find the square root of the resulting number.

Answer 1

The prime factorization of 2400 =(2 × 2) × (2 × 2) × 2 × (5 × 5) × 3

∴ 2,3 are needed to form a pair 

∴ 2 × 3 = 6 

∴ 6 should be multiplied with 2400 then we will get a perfect square number. 

∴ 2400 × 6 = 14400

∴ \(\sqrt {14400}\) = 120