Perfect Squares and Cubes Table
This reference table lists perfect squares and perfect cubes for commonly used integers. It is designed for fast lookup, verification, and pattern recognition in mathematics, science, and technical problem-solving.
Reference Values
The table below shows each integer n, its square (n²), and its cube (n³). These values frequently appear in algebraic manipulation, factorization, geometry, and numerical estimation.
| n | n² (Perfect Square) | n³ (Perfect Cube) |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 8 |
| 3 | 9 | 27 |
| 4 | 16 | 64 |
| 5 | 25 | 125 |
| 6 | 36 | 216 |
| 7 | 49 | 343 |
| 8 | 64 | 512 |
| 9 | 81 | 729 |
| 10 | 100 | 1000 |
| 11 | 121 | 1331 |
| 12 | 144 | 1728 |
| 13 | 169 | 2197 |
| 14 | 196 | 2744 |
| 15 | 225 | 3375 |
| 16 | 256 | 4096 |
| 17 | 289 | 4913 |
| 18 | 324 | 5832 |
| 19 | 361 | 6859 |
| 20 | 400 | 8000 |
How to Use This Table
- Quickly identify whether a number is a perfect square or cube
- Simplify radicals and exponent expressions
- Recognize factor patterns in algebraic equations
- Verify numerical results during calculations
- Support mental math and estimation
Definitions
A perfect square is a number that can be written as n², where n is an integer.
A perfect cube is a number that can be written as n³, where n is an integer.