The easiest way to do it, is to break the number in question into its PRIME factors:
sqrt(-72)=sqrt(2 X 2 X 2 X 3 X 3 X -1). Now, for every pair of numbers you have INSIDE the bracket, select one of them OUTSIDE the bracket. So, we take one 2 X one 3=6. Out of three 2's, that leaves one 2 INSIDE the bracket. And, since sqrt(-1)=i, then we have: 6i sqrt(2).