Symbols:Arithmetic and Algebra/General Root

Square Root

$\sqrt [r] x$

Let $x, y \in \R_{\ge 0}$ be positive real numbers.

Let $n \in \Z$ be an integer such that $n \ne 0$.

Then $y$ is the positive $n$th root of $x$ if and only if:

$y^n = x$

and we write:

$y = \sqrt[n] x$

Using the power notation, this can also be written:

$y = x^{1/n}$

Note that the overline is technically an example of a vinculum, enclosing the argument of $\surd$ in parenthesis.

The $\LaTeX$ code for \(\sqrt [r] x\) is \sqrt [r] x .

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Appendix: Table $7$: Common signs and symbols: radical