# Cube Root Calculator

## Calculator Use

Use this calculator to find the cube root of positive or negative numbers. Given a number
*x*, the cube root of *x* is a number *a* such that
*a ^{3} = x*.

If *x* is positive *a* will be positive. If *x* is negative
*a* will be negative. The Cube Root Calculator is a specialized form of our common
Radicals Calculator.

## Example Cube Roots

- The 3rd root of 64, or 64 radical 3, or the cube root of 64 is written as \( \sqrt[3]{64} = 4 \).
- The 3rd root of -64, or -64 radical 3, or the cube root of -64 is written as \( \sqrt[3]{-64} = -4 \).
- The cube root of 8 is written as \( \sqrt[3]{8} = 2 \).
- The cube root of 10 is written as \( \sqrt[3]{10} = 2.154435 \).

## What is a Cube Root as an Exponent?

The cube root of *x* is the same as
*x* raised to the 1/3 power. This is written as \( \sqrt[3]{x} = x^{\frac{1}{3}} \).

## What is a Cube Root of a Negative Number?

The common definition of the cube root of a negative number is:

*(-x) ^{1/3}* =

*-(x*

^{1/3})First take the cube root of the number and then make it negative.

### Example Cube Roots of Negative Numbers

- The cube root of -27 is written as \( \sqrt[3]{-27} = -3 \).
- The cube root of -8 is written as \( \sqrt[3]{-8} = -2 \).
- The cube root of -64 is written as \( \sqrt[3]{-64} = -4 \).

### Cube Roots Resulting in the Integers 1 Through 10

- Cube root of 1 is 1
- Cube root of 8 is 2
- Cube root of 27 is 3
- Cube root of 64 is 4
- Cube root of 125 is 5
- Cube root of 216 is 6
- Cube root of 343 is 7
- Cube root of 512 is 8
- Cube root of 729 is 9
- Cube root of 1000 is 10

To calculate fractional exponents use our calculator for Fractional Exponents.

### References

Weisstein, Eric W. "Cube Root." From
*MathWorld* -- A Wolfram Web Resource.
Cube Root

Math is Fun Cube Roots