Cube Root Calculator
The cube root of a whole number, a decimal or a fraction: the exact form with triples of prime factors taken out of the root, and the decimal value
Cube Root Calculator
Cube Root
∛N is the number whose cube is N. There is exactly one for every N, and for a negative N it is negative.
Example: ∛54
∛54 = 3∛2 ≈ 3.7798
- Prime factors
- 54 = 2 × (3 × 3 × 3) = 2 × 3³
- Take out of the root
- ∛54 = ∛(3³ × 2) = 3∛2
- Between cubes
- 3³ = 27 < 54 < 64 = 4³, so 3 < ∛54 < 4 and ∛54 ≈ 3.7798
| N | ∛N |
|---|---|
| 1 | 1 |
| 8 | 2 |
| 27 | 3 |
| 64 | 4 |
| 125 | 5 |
| 216 | 6 |
| 343 | 7 |
| 512 | 8 |
| 729 | 9 |
| 1,000 | 10 |
| 1,331 | 11 |
| 1,728 | 12 |
| 2,197 | 13 |
| 2,744 | 14 |
| 3,375 | 15 |
| 4,096 | 16 |
| 4,913 | 17 |
| 5,832 | 18 |
| 6,859 | 19 |
| 8,000 | 20 |
| x | ∛x |
|---|---|
| 0.001 | 0.1 |
| 0.008 | 0.2 |
| 0.027 | 0.3 |
| 0.064 | 0.4 |
| 0.125 | 0.5 |
| 1/8 | 1/2 = 0.5 |
| 1/27 | 1/3 ≈ 0.3333 |
| 8/27 | 2/3 ≈ 0.6667 |
| 64/125 | 4/5 = 0.8 |
Common mistakes
- A cube root is not division by 3: ∛27 = 3, while 27 ÷ 3 = 9.
- A negative number has a cube root (∛(−8) = −2), but Excel gives #NUM! for =(-8)^(1/3), and many calculators give an error for (−8)^(1/3). Take the root of the absolute value and put the minus in front: =-(8^(1/3)) gives −2.
- The cube root is not the cube: ∛8 = 2, while 8³ = 512.
See Also
- Square Root Calculator - Calculate the square root of any number
- Simplify Square Root Calculator - Write any square root in simplest radical form, step by step
- Prime Factorization - Prime Factorization Calculator
- Scientific Calculator with Memory & History - Free Engineering Calculator Online with Memory Function, Operation History, Logarithms & Trigonometry. Similar to ti-83, ti-84, ti-89
FAQ
How to find a cube root without a calculator?
Factor the number into primes and take every triple of equal factors out of the root: ∛125 = 5 because 125 = 5 × 5 × 5. If the number is not a perfect cube, bracket it between neighbouring cubes: 3³ = 27 < 54 < 64 = 4³, so 3 < ∛54 < 4 and ∛54 ≈ 3.7798.
Can a negative number have a cube root?
Yes: ∛(−8) = −2, because (−2)³ = (−2) × (−2) × (−2) = −8. A cube keeps the sign, so every negative number has exactly one cube root, and it is negative. A square root of a negative number does not exist among real numbers.
How to simplify a cube root?
Write the number as a product of primes; each triple of equal primes is a cube and comes out of the root as one factor, the rest stays under it: ∛54 = ∛(3³ × 2) = 3∛2, ∛432 = ∛(2³ × 3³ × 2) = 2 × 3 × ∛2 = 6∛2. So ∛54 = 3∛2 ≈ 3.7798.