Surds. When we can't simplify a number to remove a square root (or cube root etc) then it is a
surd. Example: √2 (square root of 2) can't be simplified further so it is a
surd. Example: √4 (square root of 4) can be simplified (to 2), so it is not a
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.