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Cube Root

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.

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Tag(s) : Symbolic Computation, Functions

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# Cube Root

## Cube Root Calculator

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.

### How to calculate a cube root?

Calculating a cubic root is not simple to do by hand except for simple 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)

### What is a cubic number?

A cubic number is the cube of an integer.

Example: 2 is an integer, 2^3 = 2*2*2 = 8 then 8 is a square number.

If the cube root of a number x is an integer, 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

### How to compute a cube root on a calculator?

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)

### What is the cube root of unity (1)?

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

### What does cbrt mean?

In some software, cbrt stands for cube root.

Example: cbrt(8)=2