1: \(A=\sqrt{\dfrac{2}{3}}-\sqrt{24}+2\cdot\sqrt{\dfrac{3}{8}}+\sqrt{\dfrac{1}{6}}\)
\(=\sqrt{\dfrac{6}{9}}-2\sqrt{6}+2\cdot\sqrt{\dfrac{6}{16}}+\sqrt{\dfrac{6}{36}}\)
\(=\dfrac{1}{3}\sqrt{6}-2\sqrt{6}+\dfrac{1}{2}\sqrt{6}+\dfrac{1}{6}\sqrt{6}\)
\(=-\sqrt{6}\)
2: \(A=\sqrt{150}+\sqrt{96}+\dfrac{9}{2}\cdot\sqrt{2\dfrac{2}{3}}-\sqrt{6}\)
\(=5\sqrt{6}+4\sqrt{6}+\dfrac{9}{2}\cdot\sqrt{\dfrac{8}{3}}-\sqrt{6}\)
\(=8\sqrt{6}+\dfrac{9}{2}\cdot\dfrac{2\sqrt{2}}{\sqrt{3}}\)
\(=8\sqrt{6}+3\sqrt{3}\cdot\sqrt{2}=11\sqrt{6}\)
3: \(A=2\sqrt{45}+\sqrt{32}-2\sqrt{20}-\dfrac{9}{2}\cdot\sqrt{8}\)
\(=2\cdot3\sqrt{5}+4\sqrt{2}-2\cdot2\sqrt{5}-\dfrac{9}{2}\cdot2\sqrt{2}\)
\(=6\sqrt{5}-4\sqrt{5}+4\sqrt{2}-9\sqrt{2}\)
\(=2\sqrt{5}-5\sqrt{2}\)
4: \(A=\sqrt{75}-\dfrac{1}{2}\cdot\sqrt{48}+\sqrt{300}-\sqrt{147}\)
\(=5\sqrt{3}-\dfrac{1}{2}\cdot4\sqrt{3}+10\sqrt{3}-7\sqrt{3}\)
\(=8\sqrt{3}-2\sqrt{3}=6\sqrt{3}\)
5: \(A=\sqrt{54}+2\sqrt{24}-\dfrac{3}{2}\cdot\sqrt{96}-\sqrt{216}\)
\(=3\sqrt{6}+2\cdot2\sqrt{6}-6\sqrt{6}-\dfrac{3}{2}\cdot4\sqrt{6}\)
\(=-3\sqrt{6}+4\sqrt{6}-6\sqrt{6}\)
\(=-5\sqrt{6}\)
6: \(A=3\sqrt{50}-2\sqrt{75}-4\cdot\dfrac{\sqrt{54}}{\sqrt{3}}-3\sqrt{\dfrac{1}{3}}\)
\(=3\cdot5\sqrt{2}-2\cdot5\sqrt{3}-4\cdot\sqrt{18}-\sqrt{3}\)
\(=15\sqrt{2}-10\sqrt{3}-12\sqrt{2}-\sqrt{3}\)
\(=3\sqrt{2}-11\sqrt{3}\)
