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Square numbers and cube numbers from 1 to 30
Squares from 1 to 30: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400 … 900. Full table with cubes, quick tricks and square roots.
A square number is a number times itself: 7² = 7 × 7 = 49. A cube number is a number times itself three times: 4³ = 4 × 4 × 4 = 64. Knowing the squares up to 30 and cubes up to 10 or more makes fractions, algebra, Pythagoras and exam arithmetic much faster.
Table of squares and cubes, 1 to 30
| n | n² (square) | n³ (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 | 1,000 |
| 11 | 121 | 1,331 |
| 12 | 144 | 1,728 |
| 13 | 169 | 2,197 |
| 14 | 196 | 2,744 |
| 15 | 225 | 3,375 |
| 16 | 256 | 4,096 |
| 17 | 289 | 4,913 |
| 18 | 324 | 5,832 |
| 19 | 361 | 6,859 |
| 20 | 400 | 8,000 |
| 21 | 441 | 9,261 |
| 22 | 484 | 10,648 |
| 23 | 529 | 12,167 |
| 24 | 576 | 13,824 |
| 25 | 625 | 15,625 |
| 26 | 676 | 17,576 |
| 27 | 729 | 19,683 |
| 28 | 784 | 21,952 |
| 29 | 841 | 24,389 |
| 30 | 900 | 27,000 |
Tricks for squaring in your head
- Numbers ending in 5: multiply the tens digit by the next number, then write 25. 35² → 3 × 4 = 12, so 1225. 85² → 8 × 9 = 72, so 7225.
- Numbers near 50: 48² is 2 less than 50, so take 25 − 2 = 23 and write 2² = 04 after it: 2304. For 53², take 25 + 3 = 28 and write 3² = 09: 2809.
- Next square from the last one: (n + 1)² = n² + n + (n + 1). From 20² = 400, 21² = 400 + 20 + 21 = 441.
How to spot perfect squares
A perfect square never ends in 2, 3, 7 or 8. So 47 and 128 cannot be perfect squares. (A number ending in 1, 4, 5, 6, 9 or 0 might be one; check it.)
Square roots
Reading the table backwards gives square roots: √625 = 25 because 25² = 625, and the cube root ∛1728 = 12 because 12³ = 1728.
Practise
- Mental maths practice: choose the squares topic.
- Maths Meteors, which includes square numbers at every level.
- Squares and cubes worksheets and square roots worksheets with answer keys.
Common questions
What are the square numbers from 1 to 100?
1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. These are 1² to 10².
What is the square of 25?
625, because 25 × 25 = 625.
What is the cube of 12?
1,728, because 12 × 12 × 12 = 1,728.
Which numbers are both squares and cubes?
Numbers that are sixth powers: 1, 64 (8² and 4³) and 729 (27² and 9³).
This guide is general information. For exams, follow your school, teacher and official exam board, and use your own judgement about what suits your child.