Whether you are a student tackling algebra, a programmer optimizing an algorithm, or a math enthusiast, having a quick reference for square numbers is an essential tool.
What is a Square Number?
A square number is the product of an integer multiplied by itself. Mathematically, it is represented as n².
Square Numbers Table: 1 to 30
| Number (n) | Square (n²) | Number (n) | Square (n²) |
|---|---|---|---|
| 1 | 1 | 16 | 256 |
| 2 | 4 | 17 | 289 |
| 3 | 9 | 18 | 324 |
| 4 | 16 | 19 | 361 |
| 5 | 25 | 20 | 400 |
| 6 | 36 | 21 | 441 |
| 7 | 49 | 22 | 484 |
| 8 | 64 | 23 | 529 |
| 9 | 81 | 24 | 576 |
| 10 | 100 | 25 | 625 |
| 11 | 121 | 26 | 676 |
| 12 | 144 | 27 | 729 |
| 13 | 169 | 28 | 784 |
| 14 | 196 | 29 | 841 |
| 15 | 225 | 30 | 900 |
Pro Tip: Perfect squares only end in 0, 1, 4, 5, 6, or 9. If a number ends in 2, 3, 7, or 8, it is not a perfect square!
Major Benchmarks up to 200
As numbers get larger, these specific squares are helpful for mental estimations:
- 40²: 1,600
- 50²: 2,500
- 100²: 10,000
- 150²: 22,500
- 200²: 40,000
Why Memorize Squares?
Recognizing these values helps with:
- Speed: Solve problems faster during timed exams.
- Square Roots: Identifying a square makes finding the root instant.
- Geometry: Calculate the area of squares and circles (πr²) more efficiently.