1967 AHSME Problem 31

Let D=a^2+b^2+c^2, where a, b, are consecutive integers and c=ab. Then \sqrt{D} is:

\begin{array}{l} \textbf{(A)}\ \text{always an even integer}\qquad \textbf{(B)}\ \text{sometimes an odd integer, sometimes not}\\ \textbf{(C)}\ \text{always an odd integer}\qquad \textbf{(D)}\ \text{sometimes rational, sometimes not}\\ \textbf{(E)}\ \text{always irrational} \end{array}

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