Answer
$2x\sqrt{2x}$
Work Step by Step
$\frac{\sqrt{24x^{4}}}{{\sqrt{3x}}}$
By the quotient rule for square roots
$=\sqrt{\frac{24x^{4}}{3x}}$
$=\sqrt{8x^{3}}$
$=\sqrt{4 \cdot 2 \cdot x^{2} \cdot x}$
$=\sqrt{4} \cdot \sqrt{x^{2}} \cdot \sqrt{2x}$
$=2x\sqrt{2x}$
