[tex]\displaystyle\\
\sqrt3(2-\sqrt2)+\sqrt2(\sqrt3-\sqrt6)=\\\\
=2\sqrt3-\sqrt6+\sqrt6-\sqrt2\sqrt6=\\\\
=2\sqrt3-\sqrt6+\sqrt6-\sqrt2 \cdot\sqrt2\sqrt3=\\\\
=\underline{2\sqrt3}-\underline{\underline{\sqrt6}}+\underline{\underline{\sqrt6}}-\underline{2\sqrt3}=0
[/tex]
