On March 11, 2002, Elizabeth discovered that the difference between two square numbers is the sum of their square roots.

Another way of looking at this is:

(x + 1)² = x² + 2x + 1 = x² + (x + (x + 1))

This can be generalized:

(x + k)² = x² + 2kx + k² = x² + k(x + (x + k))

In particular, if x=48 and k=4, we get:

52² = (48 + 4)² = 48² + 4(48 + (48 + 4)) = 2304 + 4(100) = 2704

Another way of looking at this is geometrically: