Answer
$-5\sqrt{3}$
Work Step by Step
Simplify each radical by factoring the radicand such that one of the factors is a perfect square:
$2\sqrt{12}-3\sqrt{27}\\
=2\sqrt{4\cdot 3}-3\sqrt{9\cdot 3}\\
=2\sqrt{2^2\cdot 3}-3\sqrt{3^2\cdot 3}$
Use the rule $\sqrt{a\cdot b}=\sqrt{a} \cdot \sqrt{b}$ then simplify:
$=2\sqrt{2^2}\cdot \sqrt{3}-3\sqrt{3^2}\cdot \sqrt{3}$
$=2\cdot2\cdot \sqrt{3}-3\cdot3\cdot \sqrt{3}$
$=4\sqrt{3}-9\cdot \sqrt{3}$
Factor out $\sqrt{3}$ then simplify.
$=\sqrt{3}(4-9)$
$=\sqrt{3}(-5)$
$=-5\sqrt{3}$
Hence, the correct answer is $-5\sqrt{3}$.
