I remember reading how Bethe taught Feynman how to square numbers around 50 in his head.

1) Start at 50^2 = 2500. 2) Pick a number, determine how far away it is from 50, call it N (N can be negative). 3) Multiply N by 100, add that number to 2500. 4) Square N, add that number to your current total.

For example, 52^2. 1) Start at 2500. 2) N = 2. 3) N100 = 200. 2500 + 200 = 2700. 4) N^2 = 4. 2700 + 4 = 2704.

Example when N is negative: 47^2. 1) Start at 2500. 2) N = -3. 3) N100 = -300. 2500 + (-300) = 2200. 4) N^2 = 9. 2200 + 9 = 2209.