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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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.

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)

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.

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 |

On a calculator that supports exponentiation ^ (TI-82,83 or Casio) it is possible to calculate number^(1/3) or number^0.33333333 which is equivalent according to the formula $$ \forall x \in\mathbb{R}_+^* \quad \sqrt[3]x = x^{\frac{1}{3}} $$

Formula is the same with Excel : A1^(1/3)

**Cube root** of 1 is 1 becase $ \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

dCode retains ownership of the source code of the script Cube Root online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Cube Root script for offline use on PC, iPhone or Android, ask for price quote on contact page !

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

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