gives the real-valued cube root of x.
- CubeRoot[x] returns the real-valued cube root for real-valued x.
- For symbolic x in CubeRoot[x], x is assumed to be real valued.
- CubeRoot can be evaluated to arbitrary numerical precision.
- CubeRoot automatically threads over lists.
- In StandardForm, CubeRoot[x] formats as .
- can be entered as cbrt.
- ∛z can also be used for input. The ∛ character is entered as cbrti or \[CubeRoot].
Examplesopen allclose all
Basic Examples (5)
Numerical Evaluation (4)
The precision of the output tracks the precision of the input:
Evaluate efficiently at high precision:
CubeRoot threads elementwise over lists and matrices:
Specific Values (4)
Plot the CubeRoot function:
Visualize the absolute value and argument (sign) of :
The function has the same absolute value but a different argument for :
Function Properties (9)
CubeRoot is defined on the real numbers:
The range of CubeRoot is all real numbers:
Enter a ∛ character as \[CubeRoot], followed by a number:
is neither non-negative nor non-positive:
is continuous on the reals but has a singularity at :
It is singular because it is not differentiable:
Series Expansions (4)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
General term in the series expansion using SeriesCoefficient:
The first-order Fourier series:
Function Identities and Simplifications (3)
Products can be combined using FullSimplify:
CubeRoot commutes with integer exponentiation:
Properties & Relations (4)
Wolfram Research (2012), CubeRoot, Wolfram Language function, https://reference.wolfram.com/language/ref/CubeRoot.html (updated 2020).
Wolfram Language. 2012. "CubeRoot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/CubeRoot.html.
Wolfram Language. (2012). CubeRoot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CubeRoot.html