Answer
$2x\sqrt{2x}$
Work Step by Step
RECALL:
(i) For any non-negative real numbers $a$ and $b$,
$\sqrt{\dfrac{a}{b}} = \dfrac{\sqrt{a}}{\sqrt{b}}$ and $\dfrac{\sqrt{a}}{\sqrt{b}} = \sqrt{\dfrac{a}{b}}$.
(ii) For any non-negative real number $a$, $\sqrt{a^2}=a$.
Use rule (i) above to obtain
$\require{cancel}
\sqrt{\dfrac{24x^4}{3x}}
\\=\sqrt{\dfrac{\cancel{24}8\cancel{x^4}x^3}{\cancel{3}\cancel{x}}}
\\=\sqrt{8x^3}.$
Factor the radicand so that one factor is a perfect square to obtain
$\sqrt{4x^2(2x)}
\\=\sqrt{(2x)^2(2x)}.$
Use rule (i) above to obtain
$\sqrt{(2x)^2} \cdot \sqrt{2x}.$
Use rule (ii) above to obtain
$2x\sqrt{2x}.$
