Works even better for squares ending in 5 because you'll round up and down to multiples of ten which means the number ends in 00 and you'll always be adding 25.

So:

  35 squared is 4x3 x100 = 12 00 + 25 = 1225

  45 squared is 5x4 x100 = 20 00 + 25 = 2025

  55 squared is 6x5 x100 = 30 00 + 25 = 3025

When I heard about this trick it was referred to as vedic, hindu or indian math, but I don't know if that's actually historically/geographically accurate or not. There's some Japanese nintendo DS games that aim to train you in it, I think it was a bit of a craze over there.