Cube Root Calculator
The cube root of a number x is a value a such that a³ = x. In other words, you are looking for the number that, multiplied by itself three times, gives you x. Cube roots can be positive, negative, or zero, unlike square roots.
Tip: To estimate a cube root without a calculator, find the two perfect cubes the number falls between. For example, ∛50 is between ∛27=3 and ∛64=4, closer to 4.
- 1Express the number as a product of prime factors
- 2Group prime factors into sets of three
- 3Take one factor from each group of three
- 4Multiply the results — that is the cube root
Cube root of a negative number
Unlike square roots, cube roots of negative numbers are real. ∛(−x) = −(∛x). For example, ∛(−8) = −2 because (−2)³ = −8.
Cube root as an exponent
The cube root can be written as a fractional exponent: ∛x = x^(1/3). This is useful in algebra and calculus.
| n | n³ | ∛(n³) |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 8 | 2 |
| 3 | 27 | 3 |
| 4 | 64 | 4 |
| 5 | 125 | 5 |
| 6 | 216 | 6 |
| 7 | 343 | 7 |
| 8 | 512 | 8 |
| 9 | 729 | 9 |
| 10 | 1,000 | 10 |
| 11 | 1,331 | 11 |
| 12 | 1,728 | 12 |
| 13 | 2,197 | 13 |
| 14 | 2,744 | 14 |
| 15 | 3,375 | 15 |
Fun Fact
Cube roots appear in physics when calculating the edge length of a cube from its volume, or the radius of a sphere from its volume (V = 4/3πr³ → r = ∛(3V/4π)).
References