Shortcuts
To square a number near 50, use (50 − d)² = 2,500 − 100d + d². To square any two-digit number, split it: (a + b)² = a² + 2ab + b². Unit digits also help: a perfect square can only end in 0, 1, 4, 5, 6 or 9.
Worked examples
- 47² = (50 − 3)² = 2,500 − 300 + 9 = 2,209
- 13³ = 2,197
- √1,764 = 42, since 42² = 1,764
- ∛4,096 = 16, since 16³ = 4,096
Build a habit
Learn squares to 30 and cubes to 15. Revisit them in a two-minute daily drill. For application, see simplification questions and mensuration.
