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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

### What is a cube root? (Definition)

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 $n^{1/3}$.

### How to calculate a cube root?

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)

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

On a calculator, use the exponent button and the formula: $\sqrt[3]{x} = x^{1/3}$

Example: Calculate the cube root of 64 on a calculator by typing 64 ^ (1/3) = (answer is 4)

On Casio or Texas Instrument TI, the button exponent is often written $\boxed{y^x}$

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

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)

### How to simplify a cube root?

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)

### What is a cubic number?

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

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

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

### 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

### How to write a cube root?

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

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