Tool to compute a cube root. The cube root for a number N, is the number that, multiplied by itself than again by itself, equals N.

Cube Root - dCode

Tag(s) : Symbolic Computation, Functions

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The cube root of a number $ n $ is any number $ x $ solution of the equation: $ x^3 = n $. The cube root of $ n $ is denoted $ \sqrt[3]{n} $ or $ n^{1/3} $.

Calculating a cubic root is not easy to do by hand except for usual values such as: $ \sqrt[3]{1} = 1 $, $ \sqrt[3]{8} = 2 $, $ \sqrt[3]{27} = 3 $, $ \sqrt[3]{64} = 4 $, $ \sqrt[3]{125} = 5 $, $ \sqrt[3]{1000} = 10 $

dCode software allows positive of negative numbers (complex roots) and answers an exact value or an approximate one (the precision can be adjusted by defining the precision: a minimum number of significant digits)

On a spreadsheet like Microsoft Excel, use the same formula as for a calculator, for a value in `A1` write `A1^(1/3)` or `POWER(A1;1/3)`

The root simplifier will attempt to factor the expression under the root with a perfect cube.

__Example:__ $ \sqrt[3]{8a} = 2\sqrt[3]{a} $ (the $ 8 $ has been extracted from the root)

A cubic number is the cube of an integer (cubed value).

__Example:__ $ 2 $ is an integer, $ 2^3 = 2 \times 2 \times 2 = 8 $ then $ 8 $ is a square number.

If the cube root of a number $ x $ is an integer (relative, without decimal part), then $ x $ is a cubic number.

The first perfect cubes are:

1^3 | 1 |

2^3 | 8 |

3^3 | 27 |

4^3 | 64 |

5^3 | 125 |

6^3 | 216 |

7^3 | 343 |

8^3 | 512 |

9^3 | 729 |

10^3 | 1000 |

Cube root of 1 is 1 because $ \sqrt[3]1 = 1^{\frac{1}{3}} = 1 $

In some software, `cbrt` stands for *cube root* abbreviation `cb` of `cube` and `rt` for `root`, similar to `sqrt` for *square root*.

__Example:__ `cbrt(8)=2`

The Unicode standard proposes the symbol U+221B `∛`

In LaTeX language, write `\sqrt[3]{x}`

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*Cube Root* on dCode.fr [online website], retrieved on 2022-10-05,

cube,root,cbrt,simplify,sqrt,calculator,cubed

https://www.dcode.fr/cube-root

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