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Evaluate square root
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Cube root calculator

- By Dr. Minas E. Lemonis, PhD - Updated: March 3, 2019

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

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

cbrt-graph

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

See also
Evaluate square root
Evaluate n-th root
Evaluate n-th power
Evaluate log10x
Evaluate sin(x)
All evaluation tools