Answer
$4x\sqrt{5}$
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
$\sqrt{10x(8x)}
\\=\sqrt{80x^2}.$
Factor the radicand so that one of the factors is a perfect square to obtain
$\\\sqrt{16x^2(5)}
\\=\sqrt{(4x)^2(5)}.$
Use rule (i) above to obtain
$\sqrt{(4x)^2} \cdot \sqrt{5.}$
Use rule (ii) above to obtain
$4x\sqrt{5}.$
