# How do you simplify sqrt (x^4)?

Apr 4, 2016

$\pm {x}^{2}$

#### Explanation:

${a}^{\frac{1}{N}}$ has N values that are the roots of ${a}^{N} = 1$

The roots might include complex values that occur in conjugate pairs.

Very briefly, $\sqrt{1} = \pm 1$.
$\sqrt{{x}^{4}} = {\left({x}^{4}\right)}^{\frac{1}{2}}$ has two values $\pm {x}^{2}$.
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