Answer
$36\sqrt{6}$.
Work Step by Step
The given expression is
$=\sqrt{3}(8\sqrt{2}+7\sqrt{32})$
Factor as square terms.
$=\sqrt{3}(8\sqrt{2}+7\sqrt{16\cdot 2})$
Use product property of square roots.
$=\sqrt{3}(8\sqrt{2}+7\sqrt{16}\cdot \sqrt{2})$
Use $16=4^2$.
$=\sqrt{3}(8\sqrt{2}+7\sqrt{4^2}\cdot \sqrt{2})$
Simplify.
$=\sqrt{3}(8\sqrt{2}+7\cdot 4\sqrt{2})$
$=\sqrt{3}(8\sqrt{2}+28\sqrt{2})$
Use distributive property.
$=\sqrt{3}\cdot \sqrt{2}(8+28)$
Add.
$=\sqrt{3}\cdot \sqrt{2}(36)$
Use product property of square roots.
$=\sqrt{3\cdot 2}(36)$
Simplify.
$=\sqrt{6}(36)$
$=36\sqrt{6}$.
