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

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

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