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A really nice problem. I like how you used the quadratic formula and simplified the answer algebraically. I'm always trying to keep students from rushing to their calculators. I was a bit surprised that you didn't take advantage of difference of squares when you got to Sqrt( 31^2 - 1). It would be a lot easier to work with Sqrt((31+1)(31-1) = Sqrt(32 x 30). The factoring is half done.
