The fast method
⚡
d = -3. 10000 + (-600) + 9 = 9409.
How it works
Write the number as 100 + d, then calculate 10000 + 200d + d². This is the identity (a+b)² = a² + 2ab + b² with a = 100.
Why it works
This is the identity (a+b)² = a² + 2ab + b² with a = 100.
Use it when
Works above and below 100; d is negative below 100.
Watch out for
The final d² term is always non-negative.
Verified examples
Example 1
Find 97²
d = -3. 10000 + (-600) + 9 = 9409.
9409Example 2
Find 103²
d = 3. 10000 + (600) + 9 = 10609.
10609Example 3
Find 108²
d = 8. 10000 + (1600) + 64 = 11664.
11664