Answer
$7\sqrt{7}-5\sqrt{14}$
Work Step by Step
The given expression is
$=3\sqrt{7}-5\sqrt{14}+2\sqrt{28}$
Factor as square terms.
$=3\sqrt{7}-5\sqrt{14}+2\sqrt{4\cdot 7}$
Use product property of square roots.
$=3\sqrt{7}-5\sqrt{14}+2\sqrt{4}\cdot \sqrt{7}$
Use $\sqrt {4}=2$.
$=3\sqrt{7}-5\sqrt{14}+2\cdot 2\sqrt{7}$
$=3\sqrt{7}-5\sqrt{14}+4\sqrt{7}$
Use commutative property of addition.
$=3\sqrt{7}+4\sqrt{7}-5\sqrt{14}$
Use distributive property.
$=(3+4)\sqrt{7}-5\sqrt{14}$
Add.
$=7\sqrt{7}-5\sqrt{14}$
