Fast Squaring Tricks
Quick methods for squaring numbers ending in 5 and numbers close to a convenient base.
Ending in 565² = 4,225
6 × 7 = 42
Append 25 → 4,225
Append 25 → 4,225
Why: (10n+5)² = 100n(n+1)+25.
Near 10098² = 9,604
98 − 2 = 96
2² = 4
96 | 04 = 9,604
2² = 4
96 | 04 = 9,604
Why: (100−d)² = 100(100−2d)+d².
Difference of squares52 × 48 = 2,496
50² − 2²
2,500 − 4 = 2,496
2,500 − 4 = 2,496
Why: (a+b)(a−b)=a²−b².