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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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Cube Root -

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 easy to do by hand except for usual values such as : $\sqrt{1} = 1$, $\sqrt{8} = 2$, $\sqrt{27} = 3$, $\sqrt{64} = 4$, $\sqrt{125} = 5$, $\sqrt{1000} = 10$

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)

### How to simplify a cube root?

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

Example: $\sqrt{8a} = 2 \sqrt{a}$ (the $8$ has been extracted from the root)

### What is a cubic number?

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

### 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 $$\forall x \in\mathbb{R}_+^* \quad \sqrtx = x^{\frac{1}{3}}$$

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

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

Cube root of 1 is 1 becase $\sqrt1 = 1^{\frac{1}{3}} = 1$

### What does cbrt mean?

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

## Source code

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