Squares · level 1
Squaring numbers ending in 5
Take the tens digit, multiply it by the next number up, and stick 25 on the end. That is the whole method.
Worked example: 85²
t × (t+1)72
then 2525
answer7,225
Step by step
- 1
Take the digits before the 5
t = 8
- 2
Multiply by the next number up
8 × 9 = 72
- 3
Append 25
72|25 = 7,225
85² = 7,225
The theory behind it
Intuition
A square near a reference number is (n − d)(n + d) + d², so you can always trade one hard square for one easy product plus a small square.
Common pitfalls
- ×Forgetting to add d² back.
- ×Using a reference that is not actually close, which makes d² large and slow.
In the interview
Squares appear in variance, standard deviation and compounding two periods forward.