Wanda is trying to locate the Fermat point P of triangle ABC, where A is at the origin, B is at (10,0), and C is at (3,5) (the Fermat point is the point such that the sum of its distances from the vertices of a triangle is minimized). She guesses that the point is at P = (4,2), and computes the sum of the distances from P to the vertices of triangle ABC.
If she obtains m√5 + n√10, where m and n are integers, what is m + n?