Answer
$x\sqrt[]{6}-2\sqrt[]{3xy}$
Work Step by Step
Using $a(b+c)=ab+ac$, or the Distributive Property, the given expression, $
\sqrt[]{2x}(\sqrt[]{3x}-\sqrt[]{6y})
,$ simplifies to
\begin{array}{l}
\sqrt[]{2x}(\sqrt[]{3x})-\sqrt[]{2x}(\sqrt[]{6y})
\\\\=
\sqrt[]{6x^2}-\sqrt[]{12xy}
\\\\=
\sqrt[]{(x)^2\cdot6}-\sqrt[]{4\cdot3xy}
\\\\=
\sqrt[]{(x)^2\cdot6}-\sqrt[]{(2)^2\cdot3xy}
\\\\=
x\sqrt[]{6}-2\sqrt[]{3xy}
.\end{array}
Note that all variables represent positive real numbers.
