gives the real-valued root of x.
- Surd[x,n] returns the real-valued root of real-valued x for odd n.
- Surd[x,n] returns the principal root for non-negative real-valued x and even n.
- For symbolic x in Surd[x,n], x is assumed to be real valued.
- Surd can be evaluated to arbitrary numerical precision.
- Surd automatically threads over lists.
- In StandardForm, Surd[x,n] formats as .
- can be entered as surd, and moves between the fields.
- Surd can be used with Interval and CenteredInterval objects. »
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Basic Examples (5)
Numerical Evaluation (5)
Specific Values (4)
Plot the Surd function for various orders:
Function Properties (8)
Surd[x,n] is defined for all real x when n is a positive, odd integer:
Surd is not defined for nonreal complex values:
Surd[x,n] achieves all non-negative real values when n is a positive even integer:
Surd[x,n] is not an analytic function of x for any integer n:
Compute the indefinite integral using Integrate:
With , the real vector field corresponding to the complex function is , and the trajectories that follow the field satisfy the differential equation . The implicit solution is for real , which corresponds to a family of circles that are tangent to the real axis at the origin:
For odd powers, care must be taken to ensure the first argument to Surd is non-negative:
Properties & Relations (3)
Possible Issues (1)
Neat Examples (1)
Plot a composition of Surd:
Wolfram Research (2012), Surd, Wolfram Language function, https://reference.wolfram.com/language/ref/Surd.html.
Wolfram Language. 2012. "Surd." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Surd.html.
Wolfram Language. (2012). Surd. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Surd.html