jmc

We expand $7!$: $$\sqrt{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}$$Factoring out the $4$ and the $6\cdot 3\cdot 2=36$ gives $$\boxed{12\sqrt{35}}.$$This can't be simplified any more because 35 has no square factors.