Answer
$6 \sqrt{2}+12\sqrt{5}$.
Work Step by Step
The given expression is
$=\sqrt3(2\sqrt6+4\sqrt{15})$
Use the distributive property.
$=\sqrt3(2\sqrt6)+\sqrt3(4\sqrt{15})$
Use product rule.
$=2\sqrt{6\cdot 3}+4\sqrt{15\cdot3}$
Simplify.
$=2\sqrt{18}+4\sqrt{45}$
Factor as a perfect square.
$=2\sqrt{3^2\cdot 2}+4\sqrt{3^2\cdot 5}$
Use product rule.
$=2\sqrt{3^2}\cdot \sqrt{2}+4\sqrt{3^2}\cdot \sqrt{5}$
Simplify.
$=2\cdot 3 \sqrt{2}+4\cdot 3\sqrt{5}$
Multiply.
$=6 \sqrt{2}+12\sqrt{5}$.
