\(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)=\sqrt{2-\sqrt{3}}.\sqrt{2}\left(\sqrt{3}+1\right)=\sqrt{4-2\sqrt{3}}.\left(\sqrt{3}+1\right)\)
\(=\sqrt{\left(\sqrt{3}-1\right)^2}.\left(\sqrt{3}+1\right)=\left|\sqrt{3}-1\right|.\left(\sqrt{3}+1\right)=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)=2\)
=\(\sqrt{2-\sqrt{3}.\left(\sqrt{6}+\sqrt{6}\right)}\)
\(=\sqrt{2-\sqrt{3}.\sqrt{2}\left(\sqrt{3}+1\right)}\)
\(=\sqrt{4-2\sqrt{2}.\left(\sqrt{3}+1\right)}\)
\(=\sqrt{\left(\sqrt{3}-1\right)^2}.\left(\sqrt{3}+1\right)\)
\(=\sqrt{3}-1.\left(\sqrt{3}+1\right)\)
\(=\left(\sqrt{3}-1\right).\left(\sqrt{3}+1\right)\)
\(=2\)
