1Cademy - Real Number Properties of $$n$$th Roots

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Real Number Properties of $n$ th Roots

The real number status of an $n$ th root, denoted mathematically as $\sqrt[n]{a}$ , depends entirely on whether the index $n$ is an even or odd number. When the index $n$ is an even number, the radicand $a$ must be non-negative ( $a \geq 0$ ) for the expression to evaluate to a real number; if $a < 0$ , then $\sqrt[n]{a}$ is strictly not a real number. Conversely, when the index $n$ is an odd number, the expression $\sqrt[n]{a}$ successfully evaluates to a real number for absolutely all real values of the radicand $a$ .