jmc

We need to factor out squares from 720. First we check $2^2=4$. $$720=4\cdot 180=4\cdot 4\cdot 45$$Next we check $3^2=9$. $$45=9\cdot 5$$It's obvious that 5 has no square factors (besides 1) since it is prime. So, $\sqrt{720}=\sqrt{4\cdot 4\cdot 9\cdot 5}=2\cdot 2\cdot 3\sqrt{5}=\boxed{12\sqrt{5}}$.