Square a number near 100

(100 ± d)²

The trick, step by step

1. How far from 100: 97 is 3 below.

   97−3

2. Take the distance off once more: 97 − 3 = 94. These are the hundreds.

   94

3. Then 3² = 9, written 09: 97² = 9409.

   9409

4. Above 100 add instead: 104² → 104 + 4 = 108, and 4² = 16: 10,816.

given working answer taken away

Why it works

(100 + d)² = 10000 + 200d + d² = 100(100 + 2d) + d², and 100 + 2d is the number plus the distance again.