Answer
$\sqrt{(2x)^2}$
Work Step by Step
Using $\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}$ or the quotient rule of radicals, the given expression, $
\dfrac{\sqrt{32x^3}}{\sqrt{8x}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{32x^3}{8x}}
\\\\=
\sqrt{\dfrac{4x^2\cdot\cancel{8x}}{\cancel{8x}}}
\\\\=
\sqrt{4x^2}
\\\\=
\sqrt{(2x)^2}
.\end{array}
Note that variables are assumed to have positive real numbers.
