Charts & references · 3 min read
Square Numbers and Square Roots Chart (1 to 30)
Squares from 1 to 30
| n | n² | n | n² | n | n² |
|---|---|---|---|---|---|
| 1 | 1 | 11 | 121 | 21 | 441 |
| 2 | 4 | 12 | 144 | 22 | 484 |
| 3 | 9 | 13 | 169 | 23 | 529 |
| 4 | 16 | 14 | 196 | 24 | 576 |
| 5 | 25 | 15 | 225 | 25 | 625 |
| 6 | 36 | 16 | 256 | 26 | 676 |
| 7 | 49 | 17 | 289 | 27 | 729 |
| 8 | 64 | 18 | 324 | 28 | 784 |
| 9 | 81 | 19 | 361 | 29 | 841 |
| 10 | 100 | 20 | 400 | 30 | 900 |
Square roots you will meet most
| Number | Square root (4 d.p.) | Note |
|---|---|---|
| 2 | 1.4142 | irrational |
| 3 | 1.7321 | irrational |
| 5 | 2.2361 | irrational |
| 6 | 2.4495 | irrational |
| 7 | 2.6458 | irrational |
| 8 | 2.8284 | irrational |
| 10 | 3.1623 | irrational |
| 12 | 3.4641 | irrational |
| 15 | 3.873 | irrational |
| 20 | 4.4721 | irrational |
These are irrational: their decimals never end or repeat. Use the scientific calculator for others.
Tricks
Numbers ending in 5: multiply the tens digit by one more than itself, then write 25. For 35², 3 × 4 = 12, so 1225.
Difference of squares: a² − b² = (a + b)(a − b), so 51² − 49² = 100 × 2 = 200.
Squares are sums of odd numbers: 1 + 3 + 5 + 7 = 16 = 4².
Is it a perfect square?
Check the last digit first, then estimate: √1,521 is between 30 and 40, ends in 1, so it could be 31 or 39 — and 39² = 1521.
Frequently asked questions
What is the square root of 144?
12, because 12 × 12 = 144.
Why do squares never end in 2, 3, 7 or 8?
The last digit of n² depends only on the last digit of n, and no digit squared ends in those four.
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