1982 AHSME Problem 30

Find the units digit of the decimal expansion of

(15 + \sqrt{220})^{19} + (15 + \sqrt{220})^{82}.

\textbf{(A)}\ 0\qquad \textbf{(B)}\ 2\qquad \textbf{(C)}\ 5\qquad \textbf{(D)}\ 9\qquad \textbf{(E)}\ \text{none of these}

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