GCF and differences of roots

Question

I found a problem that was asking about the GCF and the minimum difference between two roots, and I was wondering if anyone could help.

"Given two perfect squares, m and n GCF(m,n) = 4 and mn=2304. Find the minimum positive difference in their positive roots."

Thanks!

Answer 1

So $m=4a$ and $n = 4b$. If $mn = 2304$ then $16ab = 2304$, or ab = 144 find all positive perfect squares that multiply to make $144$ and go from there.