#### Answer

$\dfrac{4x}{y}$

#### Work Step by Step

The variables are assumed to be non-zero since they are also in the denominator.
RECALL:
$\dfrac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ where $a$ and $b$ are non-negative and $b\ne0.$
Use the rule above to have
$\sqrt{\dfrac{48x^3}{3xy^2}}
\\=\sqrt{\dfrac{16x^2}{y^2}}
\\=\sqrt{\left(\dfrac{4x}{y}\right)^2}
\\=\dfrac{4x}{y}.$