# Chapter R - Review of Basic Concepts - R.6 Rational Exponents - R.6 Exercises: 53

$(-4)^{1/2}$ is not a real number

#### Work Step by Step

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

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