Answer
$2x\sqrt{3}$
Work Step by Step
RECALL:
(i) For any non-negative real numbers $a$ and $b$,
$\sqrt{ab} = \sqrt{a}\cdot \sqrt{b}$ and $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$.
(ii) For any non-negative real number $a$, $\sqrt{a^2}=a$.
Use rule (i) above to obtain
$\sqrt{6x(2x)}
\\=\sqrt{12x^2}.$
Factor the radicand so that one of the factors is a perfect square to obtain
$\\\sqrt{4x^2(3)}
\\=\sqrt{(2x)^2(3)}.$
Use rule (i) above to obtain
$\sqrt{(2x)^2} \cot \sqrt{3}.$
Use rule (ii) above to obtain
$=2x\sqrt{3}$.
