Square a number near 50

(50 ± d)²

The trick, step by step

1. How far from 50: 53 is 3 above.

   53+3

2. Hundreds: 25 + 3 = 28.

   28

3. Then 3² = 9, written 09 in the last two digits: 53² = 2809.

   2809

4. Below 50 take away instead: 47² → 25 − 3 = 22, and 09: 2209.

given working answer taken away

Why it works

(50 + d)² = 2500 + 100d + d² = 100(25 + d) + d²: 25 + d hundreds, and d² at the end.