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Surd


In general, an unresolved nth root, commonly involving a radical symbol RadicalBox[x, n], is known as a surd. However, the term surd or "surd expression" (e.g., Hardy 1967, p. 25) can also be used to mean a sum of one or more irrational roots. In the mathematical literature, the term arises most commonly in the context of quadratic surds.

The term "surd" has a special meaning in the Wolfram Language, where the principal nth root of a complex number z can be found as z^(1/n) or equivalently Power[z, 1/n]. However, when x is real and only real roots are of interest, the command Surd[x, n] which returns the real-valued nth root for real x odd n and the principal nth root for nonnegative real x and even n can be used.


See also

Cube Root, nth Root, Principal Root of Unity, Radical, Square Root, Quadratic Surd

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References

Hardy, G. H. A Course of Pure Mathematics, 10th ed. Cambridge, England: Cambridge University Press, 1967.

Referenced on Wolfram|Alpha

Surd

Cite this as:

Weisstein, Eric W. "Surd." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Surd.html

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