2011 AMC 10A Problem 16

Which of the following is equal to \sqrt{9-6\sqrt{2}}+\sqrt{9+6\sqrt{2}}?

\textbf{(A)}\,3\sqrt2 \qquad\textbf{(B)}\,2\sqrt6 \qquad\textbf{(C)}\,\frac{7\sqrt2}{2} \qquad\textbf{(D)}\,3\sqrt3 \qquad\textbf{(E)}\,6

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