Question

Find the smallest positive integer such that the product of this integer and 180 is a perfect square.

Answer 1

Consider the prime factorization of 180:

`180=2^4\cdot5`

`2^4=(2^2)^2`, so you need to multiply by 5 to get another squared factor.

`180\cdot5=2^4\cdot5^2=(2^2\cdot5)^2`