===== Answer =====

C = 6

N = 25

25<sup>2</sup> = 625

There are a couple of tricks you can use for this problem. Recognize that the only two digit numbers that you can square to get a three digit number are between 10 and 31. Also recognize that the final digit needs to be repeated when squared - the only digits that do this are 0, 1, 5, and 6. So now you only need to check a few values for N: 10, 11, 15, 16, 20, 21, 25, 26, 30, and 31.

(The other trick is to just memorize squares up to 30, or remember that 5<sup>3</sup> is 625)