\(a,=4\sqrt{5}-3\sqrt{5}+9\sqrt{2}+12\sqrt{2}-5\sqrt{2}=\sqrt{5}+16\sqrt{2}\\ b,=3-\left(-2\right)+5=10\\ c,=\dfrac{\sqrt{2}}{2}+\dfrac{3\sqrt{2}}{2}-\dfrac{5\sqrt{2}}{2}-5\sqrt{2}+11\sqrt{2}+\dfrac{9\sqrt{2}}{2}-\dfrac{7\sqrt{2}}{2}\\ =\dfrac{\sqrt{2}}{2}+6\sqrt{2}=\dfrac{13\sqrt{2}}{2}\\ d,=\left(\dfrac{3\sqrt{6}}{2}+\dfrac{2\sqrt{6}}{3}-2\sqrt{6}\right)\left(\sqrt{6}-\sqrt{12}-\sqrt{6}\right)\\ =\dfrac{9\sqrt{6}+4\sqrt{6}-12\sqrt{6}}{6}\cdot\left(-\sqrt{12}\right)=\dfrac{-\sqrt{12}\cdot\sqrt{6}}{6}=\dfrac{-6\sqrt{2}}{6}=-\sqrt{2}\)
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