2011 AMC 10A Problem 19

In 1991 the population of a town was a perfect square. Ten years later, after an increase of 150 people, the population was 9 more than a perfect square. Now, in 2011, with an increase of another 150 people, the population is once again a perfect square. Which of the following is closest to the percent growth of the town's population during this twenty-year period?

\textbf{(A)}\ 42\% \qquad\textbf{(B)}\ 47\% \qquad\textbf{(C)}\ 52\%\qquad\textbf{(D)}\ 57\%\qquad\textbf{(E)}\ 62\%

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