## Precalculus (6th Edition)

$(-4)^{1/2}$ is not a real number
RECALL: (1) $a^{1/2} = \sqrt{a}$ (2) $\sqrt{9} = 3$ since $3^2=9$ (3) For any real number $a$, $a^2 \ge 0$. Use rule (1) above to obtain: $(-4)^{1/2} = \sqrt{-4}$ Note that there is no real number that when squared will give $-4$ since when a real number is squared, the result is always non-negative. Thus, $(-4)^{1/2}$ is not a real number