## Intermediate Algebra (12th Edition)

$x=\pm4\sqrt{2}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $x^2=32 ,$ take the square root of both sides (Square Root Property). Then simplify the resulting radical. $\bf{\text{Solution Details:}}$ Taking the square root of both sides (Square Root Property), the equation above is equivalent to \begin{array}{l}\require{cancel} x=\pm\sqrt{32} .\end{array} Writing the radicand as an expression that contains a factor that is a perfect power of the index and then extracting the root of that factor result to \begin{array}{l}\require{cancel} x=\pm\sqrt{16\cdot2} \\\\ x=\pm\sqrt{(4)^2\cdot2} \\\\ x=\pm4\sqrt{2} .\end{array}