Answer
$-30 \sqrt{6}$.
Work Step by Step
Multiply the numerical coeffiients together:
$(5\sqrt{8})(-3\sqrt{3})\\
=(-5\cdot 3)\sqrt{8}\cdot \sqrt{3}\\
=-15\sqrt8\cdot\sqrt3$
Use the product rule $\sqrt{a}\cdot \sqrt{b}=\sqrt{ab}, a, b>0$ to obtain:
$=-15\sqrt{8 \cdot 3}\\
=-15\sqrt{24}$
Factor the radicand so that on factor is a perfect square number.
$=-15\sqrt{4 \cdot 6}$
$=-15\sqrt{2^2 \cdot 6}$
Use the product rule.
$=-15\sqrt{2^2} \cdot \sqrt{6}$
$=-15\cdot 2 \cdot \sqrt{6}$
$=-30 \sqrt{6}$
Hence, the correct answer is $-30 \sqrt{6}$.
