Surd

The real nth root of a real x, staying real for a negative x when n is odd.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageSurd✓↗

Surd(x, n)the real nth root of x

Typed signatures

Type	Package	Applies
(number, number) -> number	combinatorics	always

Domain: Collections

Details

• Differs from x^(1/n): that gives a complex principal root for a negative x, where Surd stays on the real line whenever a real root exists.
• An even n with a negative x has no real root and is left unevaluated.

Plot

Examples

Basic #

The real cube root of -8 is -2, not a complex principal root

live ↗

In$\mathrm{Surd}(-8, 3)$Out$-2$

Scope #

For a nonnegative base, Surd agrees with Power(x, 1/n)

live ↗

In$\mathrm{Surd}(8, 3)$Out$2$

About

Examples	2
Checked against	Wolfram Language 2 agree
Crosswalk	Wolfram Language