# Cube Root Calculator

Use this calculator to easily calculate the cube root of a given number.

## What is a cube root?

The **cube root** of a number answers the question "what number can I multiply by itself twice to get this number?". It is the reverse of the exponentiation operation with an exponent of 3, so if r^{3} = x, then we say that "r is the cube root of x". Finding the root of a number has a special notation called the radical symbol: √ - which is used as it is when it comes to square roots, but gets an index number indicating the root - 3 in the case of the cube root, so it looks like so: ∛. Usually the radical spans over the entire equation for which the root is to be found. It is called a "cube" root since multiplying a number by itself twice is how one finds the volume of a cube.

Unlike the square root, there is only one unique real number root as a result from applying the cube root function for a given number and it carries the sign of the number. For example, the cube root of 8 is 2, while the cube root of -8 is -2, since 2 x 2 x 2 = 8 and -2 x -2 x -2 = -8. The real number cube root is the Principal cube root, but each real number cube root (zero excluded) also has a pair of complex conjugate cube roots, for example the other cube roots of 8 are -1 + √3*i* and -1 - ^radic;3*i*. Our calculator will only output the principal root. See the table of common roots below for more examples.

In geometrical terms, the cube root function maps the volume of a cube onto its side length.

## Properties and practical application of the cube root

Cubic roots are useful when one needs to divide an angle in three, that is - to find an angle whose measure is one third of a given angle. This operation is called angle trisection. Cube roots are used when you need to find the edge of a cube whose volume is twice that of a cube with a given edge.

Plotting the results from the cube root function, as calculated using this cube root calculator, on a graph reveals that it has the shape of half a parabola.

## Commonly used cube roots

Table of commonly encountered cube roots:

Cubic Root of | Root |
---|---|

∛1 | 1 |

∛8 | 2 |

∛27 | 3 |

∛64 | 4 |

∛125 | 5 |

∛216 | 6 |

∛1,000 | 10 |

∛1,000,000 | 100 |

∛1,000,000,000 | 1000 |

The calculations were performed using this cube root calculator.

#### Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation:

Georgiev G.Z., *"Cube Root Calculator"*, [online] Available at: https://www.gigacalculator.com/calculators/cube-root-calculator.php URL [Accessed Date: 18 Jul, 2019].