Squares & Cubes Learning Tool
| Number (a) | Square (a²) | Cube (a³) | Difference (a³ – a²) |
|---|
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Understanding Squares and Cubes
Square (a²): When you multiply a number by itself once.
Example: 5² = 5 × 5 = 25
Cube (a³): When you multiply a number by itself twice (three times total).
Example: 5³ = 5 × 5 × 5 = 125
The Difference (a³ – a²): How much bigger the cube is compared to the square.
Example: 5³ – 5² = 125 – 25 = 100
Memory Tips
- Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
- Perfect Cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
- Pattern for 5: 5² = 25, 5³ = 125 (just add 1 in front!)
- Pattern for 10: 10² = 100, 10³ = 1000 (count the zeros!)
- Notice: For numbers ≥ 2, a³ is always bigger than a²
- Special case: Only for 1, a² = a³ = 1
- Easy to remember: 6² = 36, 6³ = 216 (36 × 6 = 216)
- 9’s pattern: 9² = 81, 9³ = 729 (81 × 9 = 729)