Answer
$30\sqrt{2}$
Work Step by Step
The given expression is
$=\sqrt{6}(7\sqrt{12}-4\sqrt{3})$
Factor as square terms.
$=\sqrt{6}(7\sqrt{4\cdot 3}-4\sqrt{3})$
Use product property of square roots.
$=\sqrt{6}(7\sqrt{4}\cdot \sqrt{3}-4\sqrt{3})$
Simplify.
$=\sqrt{6}(7(2) \sqrt{3}-4\sqrt{3})$
Use distributive property.
$=\sqrt{6}\sqrt{3}(14 -4)$
Simplify.
$=\sqrt{6}\sqrt{3}(10)$
Use product property of square roots.
$=10\sqrt{6\cdot 3}$
Factor as square terms.
$=10\sqrt{9\cdot 2}$
Use product property of square roots.
$=10\sqrt{9}\cdot \sqrt{2}$
Simplify.
$=10(3)\sqrt{2}$
$=30\sqrt{2}$
