How to square numbers close to 100
Same idea as squaring near 50, anchored at a rounder number: 100² = 10000 is the easiest square there is, and numbers close to 100 can borrow that fact directly.
The rule
Let x be the distance from 100. Then:
Why it works
Expanding (100+x)² directly gives 10000 + 200x + x². The 200x term is easy because multiplying by 200 is just multiplying by 2 and shifting two places — no different from the 100x term in the close-to-50 version, just scaled up.
Worked examples
97² — x = −3. 10000 − 600 + 9 = 9409.
102² — x = +2. 10000 + 400 + 4 = 10404.
108² — x = +8. 10000 + 1600 + 64 = 11664.
94² — x = −6. 10000 − 1200 + 36 = 8836.
A note on larger deviations
Because the base is bigger here, this method stays useful over a wider range than the close-to-50 version — x up to 15–20 is still comfortable, since x² for those values is still a quick calculation.