2002 AMC 10B Problem 14

The number 25^{64}\cdot 64^{25} is the square of a positive integer N. In decimal representation, the sum of the digits of N is

\mathrm{(A) \ } 7\qquad \mathrm{(B) \ } 14\qquad \mathrm{(C) \ } 21\qquad \mathrm{(D) \ } 28\qquad \mathrm{(E) \ } 35

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