## Cube root calculator

This tool evaluates the cube root of a number: $$\sqrt[3]{x}$$. Enter the argument x below.

 x = Result: $$\sqrt[3]{x}$$ =

## Definitions

### General

The cube root of a number x, is a number r so that r3 = x. In modern notation cube root is written as $$\sqrt[3]{x}$$ or x1/3 . Any real number has one real cube root, while any non-zero real number has two complex cube roots too. The real cube root of a positive number is always positive while the real cube root of a negative number is negative. The cube root of 0 is 0.

The graph of the real cube root function is shown in the figure below. It is a monotonic function with symmetry around origin.

### Properties

The derivative of the cube root function is:

$\left(\sqrt[3] x\right)' = \frac{1}{3}x^{-2/3} = \frac{1}{3\sqrt[3]{x^2}}$

The integral of the cube root function is given by:

$\int \sqrt[3] x\, \mathrm{d}x = \frac{3x^{4/3}}{4} +C$