Answer
$8\sqrt{3}$
Work Step by Step
Factor each radicand so that one factor is a perfect square:
$\sqrt{25\cdot 3}+2\sqrt{16\cdot3}-5\sqrt{3}$
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:
$\sqrt{25\cdot3}+2\sqrt{16\cdot3}-5\sqrt{3}$
$=\sqrt{25}\cdot \sqrt{3}+2\sqrt{16}\cdot \sqrt{3}-5\sqrt{3}$
Recall that $5^2=25$ and $4^2=16$.
Thus, the expression above simplifies to:
$5\sqrt{3}+2\cdot4\sqrt{3}-5\sqrt{3}$
$=5\sqrt{3}+8\sqrt{3}-5\sqrt{3}$
$=(5+8-5)\sqrt{3}$
$=8\sqrt{3}$
