\(B=\dfrac{\sqrt{6+2\left(\sqrt{6}+\sqrt{3}+\sqrt{2}\right)}-\sqrt{6-2\left(\sqrt{6}-\sqrt{3}+\sqrt{2}\right)}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{6+2\sqrt{6}+2\sqrt{3}+2\sqrt{2}}-\sqrt{6-2\sqrt{6}+2\sqrt{3}-2\sqrt{2}}}{\sqrt{2}}\)
\(=\dfrac{\left(\sqrt{6+2\sqrt{6}+2\sqrt{3}+2\sqrt{2}}-\sqrt{6-2\sqrt{6}+2\sqrt{3}-2\sqrt{2}}\right)\sqrt{2}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{\left(6+2\sqrt{6}+2\sqrt{3}+2\sqrt{2}\right)\cdot2}-\sqrt{\left(6-2\sqrt{6}+2\sqrt{3}-2\sqrt{2}\right)\cdot2}}{2}\)
\(=\dfrac{\sqrt{12+4\sqrt{6}+4\sqrt{3}+4\sqrt{2}}-\sqrt{12-4\sqrt{6}+4\sqrt{3}-4\sqrt{2}}}{2}\)
\(=\dfrac{4}{2}\)
\(=2\)
\(C=\dfrac{\sqrt{9-6\sqrt{2}}-\sqrt{6}}{\sqrt{3}}\)
\(=\dfrac{\left(\sqrt{9-6\sqrt{2}}-\sqrt{6}\right)\sqrt{3}}{3}\)
\(=\dfrac{\sqrt{\left(9-6\sqrt{2}\right)\cdot3}-3\sqrt{2}}{3}\)
\(=\dfrac{\sqrt{27-18\sqrt{2}}-3\sqrt{2}}{3}\)
\(=\dfrac{\sqrt{\left(3-3\sqrt{2}\right)^2}-3\sqrt{2}}{3}\)
\(=\dfrac{3\sqrt{2}-3-3\sqrt{2}}{3}\)
\(=\dfrac{-3}{3}\)
\(=-1\)
