\(a,=10\sqrt{3}-4\sqrt{3}+4\sqrt{3}\)
\(=10\sqrt{3}\)
\(b,=\dfrac{2}{3}\sqrt{3}-\dfrac{3}{4}\sqrt{2}+\dfrac{2}{5}\sqrt{2}-\dfrac{1}{2}\sqrt{3}\)
\(=\left(\dfrac{2}{3}\sqrt{3}-\dfrac{1}{2}\sqrt{3}\right)+\left(\dfrac{-3}{4}\sqrt{2}+\dfrac{2}{5}\sqrt{2}\right)\)
\(=\dfrac{1}{6}\sqrt{3}-\dfrac{7}{20}\sqrt{2}\)
\(c,\left(2\sqrt{3}-2\sqrt{3}+5\sqrt{2}-\dfrac{3}{2}\sqrt{2}\right).2\sqrt{6}\)
\(=\dfrac{7\sqrt{2}}{2}.2\sqrt{6}=14\sqrt{3}\)
\(d,=\left(\dfrac{15\left(\sqrt{6}-1\right)}{\left(\sqrt{6}+1\right)\left(\sqrt{6}-1\right)}+\dfrac{4\left(\sqrt{6}+2\right)}{\left(\sqrt{6}-2\right)\left(\sqrt{6}+2\right)}-\dfrac{12\left(3+\sqrt{6}\right)}{\left(3-\sqrt{6}\right)\left(3+\sqrt{6}\right)}\right).\left(\sqrt{6}+11\right)\)
\(=\left(\dfrac{15\sqrt{6}-15}{6-1}+\dfrac{4\left(\sqrt{6}+2\right)}{6-4}-\dfrac{12\left(3+\sqrt{6}\right)}{9-6}\right)\left(\sqrt{6}+11\right)\)
\(=\left(3\sqrt{6}-3+2\sqrt{6}+4-12-4\sqrt{6}\right)\left(\sqrt{6}+11\right)\)
\(=\left(\sqrt{6}-11\right)\left(\sqrt{6}+11\right)\)
\(=6-121=-115\)
