Answer
$10x\sqrt{2x}$
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{400x^4}}{\sqrt{2x}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{400x^4}{2x}}
\\\\=
\sqrt{\dfrac{200x^3\cdot\cancel{2x}}{\cancel{2x}}}
\\\\=
\sqrt{200x^3}
\\\\=
\sqrt{100x^2\cdot2x}
\\\\=
\sqrt{(10x)^2\cdot2x}
\\\\=
10x\sqrt{2x}
.\end{array}
Note that variables are assumed to have positive real numbers.
