How to square numbers close to 50
50² is trivial — 2500. Numbers just above or below 50 can borrow that fact directly instead of being squared from scratch.
The rule
Let x be the distance from 50 (positive if above, negative if below). Then:
Why it works
This is the standard (a+b)² expansion with a = 50 fixed: (50+x)² = 2500 + 100x + x². Because a = 50 never changes, 2500 and the 100x term are both fast to produce — the only real work is x², and x is always small since you'd switch methods for numbers far from 50 anyway.
Worked examples
48² — x = −2. 2500 − 200 + 4 = 2304.
53² — x = +3. 2500 + 300 + 9 = 2809.
58² — x = +8. 2500 + 800 + 64 = 3364.
47² — x = −3. 2500 − 300 + 9 = 2209.
When it's worth using
This shortcut earns its keep roughly within ±10 of 50 — once x gets larger, x² itself starts requiring real calculation, at which point breaking the number into tens and units (the general-case method) is just as fast.