Answer
$12 \sqrt{3}$
Work Step by Step
Multiply the numerical coefficients together:
$(3\sqrt{6})(2\sqrt{2})\\
=3\cdot 2\sqrt{6}\cdot \sqrt{2}\\
=6\sqrt6\cdot\sqrt2$
Use the product rule $\sqrt{a}\cdot \sqrt{b}=\sqrt{ab}, a, b>0$ to obtain:
$=6\sqrt{6 \cdot 2}\\
=6\sqrt{12}$
Factor the radicand so that one factor is a perfect square number:
$=6\sqrt{4 \cdot 3}$
$=6\sqrt{2^2 \cdot 3}$
Use the product rule.
$=6\sqrt{2^2} \cdot \sqrt{3}\\
=6\cdot 2 \cdot \sqrt{3}\\
=12 \sqrt{3}$
Hence, the correct answer is $12 \sqrt{3}$.
