The least number by which 180 must be multiplied to make it a perfect square is:

Question: The least number by which 180 must be multiplied to make it a perfect square is:

Solution:
Prime factorization of 180 = 2 × 2 × 3 × 3 × 5
= 2² × 3² × 5¹
For a number to be a perfect square, every exponent in the prime factorization must be even.
2² ; even power
3² ; even power
5¹ ; odd power
The only odd exponent is 5. To make it even, multiply by 5.
= 180 × 5
= 900
= 30²

So the least number by which 180 must be multiplied to make it a perfect square is 5