Answer
$13\sqrt{5}$
Work Step by Step
Factor each radicand so that one factor is a perfect square:
$14\sqrt{4\cdot5}-3\sqrt{25\cdot5}$
Recall the property (pg. 367):
$\sqrt[n]{a}\cdot \sqrt[n]{b}=\sqrt[n]{ab}$ (if $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers)
Applying this property, we get:
$14\sqrt{4\cdot5}-3\sqrt{25\cdot5}$
$=14\sqrt{4}\cdot\sqrt{5}-3\sqrt{25}\cdot\sqrt{5}$
$=14\cdot2\sqrt{5}-3\cdot5\sqrt{5}$
$=28\sqrt{5}-15\sqrt{5}$
$=13\sqrt{5}$
