## Intermediate Algebra (12th Edition)

$\sqrt[n] a$ will not be a real number if $n$ is even and $a$ is negative
We know that the expression $\sqrt[n] a$ will not be a real number when both of the following two conditions are satisfied: 1. $n$ is even 2. $a$ is negative For example, we know that $\sqrt[4] -50$ is not a real number, because there is no real number $r$ such that $r^{4}=-50$. In general, we cannot find any negative numbers that can be raised to an even power to result in a positive number.