Surd

In general, an unresolved nth root, commonly involving a radical symbol , 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 th root of a complex number  can be found as z^(1/n) or equivalently Power[z, 1/n]. However, when  is real and only real roots are of interest, the command Surd[x, n] which returns the real-valued th root for real  odd  and the principal th root for nonnegative real  and even  can be used.

REFERENCES:

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