2006 AMC 10A Problem 10

For how many real values of $x$ is $\sqrt{120-\sqrt{x}}$ an integer?

$\mathrm{(A)}\ 3\qquad\mathrm{(B)}\ 6\qquad\mathrm{(C)}\ 9\qquad\mathrm{(D)}\ 10\qquad\mathrm{(E)}\ 11\qquad$

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.