1, \(A=7\sqrt{2}+4\sqrt{2}=11\sqrt{2}\)
2, \(B=2\sqrt{5}-2\sqrt{5}+9\sqrt{5}=9\sqrt{5}\)
3, \(C=3\sqrt{36}-5\sqrt{81}+\sqrt{144}=18-45+12=-15\)
4, \(D=\dfrac{13\left(3-\sqrt{3}\right)}{9-3}-\dfrac{6\sqrt{3}}{3}-\dfrac{\sqrt{6}\left(\sqrt{3}-\sqrt{2}\right)}{\sqrt{3}-\sqrt{2}}=\dfrac{39-13\sqrt{3}-12\sqrt{3}}{6}-\sqrt{6}=\dfrac{39-25\sqrt{5}}{6}-\sqrt{6}\)
5, \(E=\left(5+\sqrt{5}\right)\left(\sqrt{5}-2\right)+\sqrt{5}-1-\dfrac{11\left(2\sqrt{5}-3\right)}{11}=5\sqrt{5}-10+5-2\sqrt{5}+\sqrt{5}-1-2\sqrt{5}+3=2\sqrt{5}-6\)
6, \(F=\dfrac{2\left(11-\sqrt{5}\right)}{116}-\sqrt{\dfrac{6+2\sqrt{5}}{4}}=\dfrac{11-\sqrt{5}}{58}-\dfrac{\sqrt{5}+1}{2}=\dfrac{11-\sqrt{5}-29\sqrt{5}-29}{58}=\dfrac{-18-21\sqrt{5}}{58}\)
1: \(=7\sqrt{2}+4\sqrt{2}=11\sqrt{2}\)
2: \(=2\sqrt{5}-2\sqrt{5}+9\sqrt{5}=9\sqrt{5}\)
3: \(=\left(6\sqrt{3}-15\sqrt{3}+4\sqrt{3}\right)\cdot\sqrt{3}\)
=18-45+12
=30-45=-15
