Answer
$-\sqrt3$
Work Step by Step
$\frac{-3\sqrt2}{\sqrt6}\longrightarrow$ multiply numerator and denominator by $\sqrt6$
=$\frac{-3\sqrt2}{\sqrt6}\times\frac{\sqrt6}{\sqrt6}\longrightarrow$ simplify, multiplication property of square roots
=$\frac{-3\sqrt{12}}{\sqrt{36}}\longrightarrow$ factor perfect square out of 12
=$\frac{-3\sqrt{4\times3}}{\sqrt{36}}\longrightarrow$ multiplication property of square roots
=$\frac{-3\times\sqrt{4}\times\sqrt3}{\sqrt{36}}\longrightarrow$ simplify
=$\frac{-3\times2\times\sqrt3}{6}\longrightarrow$ simplify
=$\frac{-6\sqrt3}{6}\longrightarrow$ simplify
=$-\sqrt3$
