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principal square root

The nonnegative square root — the one the $\sqrt{\ }$ symbol always means.

The principal $n$ th root of $a$ , written $\sqrt[n]{a}$ , is the nonnegative root when $n$ is even, and the unique real root when $n$ is odd. $\sqrt{25}$ means $5$ , never $-5$ , even though both square to $25$ .

Examples

$\sqrt{25} = 5$ , not $\pm 5$ .

See also

radicand index (of a radical)

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