AMC 12 2006a Problem 10

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

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