Cube Roots Test
mediumThis test asks for the cube roots of perfect cubes, such as ∛1728 = 12. Easy goes up to ∛1000, Medium covers ∛216 to ∛8000, and Hard runs from ∛1331 to ∛27000.
Cube roots from ∛216 to ∛8000.
Cube roots look hard but follow a neat pattern: the last digit of the cube tells you the last digit of the root. The chart and tricks below show the whole method.
Perfect cubes and their cube roots (1 to 30)
| Perfect cube | Cube root | Perfect cube | Cube root |
|---|---|---|---|
| 1 | ∛1 = 1 | 4,096 | ∛4096 = 16 |
| 8 | ∛8 = 2 | 4,913 | ∛4913 = 17 |
| 27 | ∛27 = 3 | 5,832 | ∛5832 = 18 |
| 64 | ∛64 = 4 | 6,859 | ∛6859 = 19 |
| 125 | ∛125 = 5 | 8,000 | ∛8000 = 20 |
| 216 | ∛216 = 6 | 9,261 | ∛9261 = 21 |
| 343 | ∛343 = 7 | 10,648 | ∛10648 = 22 |
| 512 | ∛512 = 8 | 12,167 | ∛12167 = 23 |
| 729 | ∛729 = 9 | 13,824 | ∛13824 = 24 |
| 1,000 | ∛1000 = 10 | 15,625 | ∛15625 = 25 |
| 1,331 | ∛1331 = 11 | 17,576 | ∛17576 = 26 |
| 1,728 | ∛1728 = 12 | 19,683 | ∛19683 = 27 |
| 2,197 | ∛2197 = 13 | 21,952 | ∛21952 = 28 |
| 2,744 | ∛2744 = 14 | 24,389 | ∛24389 = 29 |
| 3,375 | ∛3375 = 15 | 27,000 | ∛27000 = 30 |
How to find cube roots quickly
- Learn the first ten cubes (1, 8, 27, 64, 125, 216, 343, 512, 729, 1000) and you can read off the small cube roots.
- The last digit of a cube gives the last digit of its root: 1 → 1, 8 → 2, 7 → 3, 4 → 4, 5 → 5, 6 → 6, 3 → 7, 2 → 8, 9 → 9, 0 → 0.
- Ignore the last three digits to find the tens digit. For ∛17576: it ends in 6, so the root ends in 6. The front part is 17, which sits between 8 (2³) and 27 (3³), so the tens digit is 2. The answer is 26.
- Another example, ∛12167: it ends in 7, so the root ends in 3. The front part is 12, between 8 and 27, so the tens digit is 2. The answer is 23.
- Prime factors also work: 1728 = 2⁶ × 3³, so ∛1728 = 2² × 3 = 12.
Frequently asked questions
What is the cube root of 27?
∛27 = 3, because 3 × 3 × 3 = 27.
What is the cube root of 1000?
∛1000 = 10, because 10 × 10 × 10 = 1000.
What is the cube root of 3375?
∛3375 = 15, because 15 × 15 × 15 = 3375. It ends in 5, so the root ends in 5, and 3 lies between 1 and 8, which puts the tens digit at 1.
How do you find a cube root without a calculator?
Ignore the last three digits to find the tens digit. For ∛17576: it ends in 6, so the root ends in 6. The front part is 17, which sits between 8 (2³) and 27 (3³), so the tens digit is 2. The answer is 26.
How is the speed maths test scored?
Each test has 10 questions. Answer 8 or more correctly to pass. Your time is recorded for the whole test, and your best time for each test and level is saved on your own device, so you can try to beat it.