3: \(=\left(3\sqrt{2}-3+4\sqrt{2}+2-4-2\sqrt{2}\right)\cdot\left(2\sqrt{2}+2\right)\)
\(=\left(5\sqrt{2}-5\right)\left(2\sqrt{2}+2\right)=2\cdot5=10\)
4: \(=\left(\sqrt{3}+\sqrt{5}\right)\cdot\sqrt{8-2\sqrt{15}}\)
\(=\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)=5-3=2\)
5: \(=9\sqrt{3}+\dfrac{1}{2}\cdot2\sqrt{3}-5\sqrt{3}+\dfrac{2}{7}\cdot7\sqrt{3}\)
\(=9\sqrt{3}+\sqrt{3}-5\sqrt{3}+2\sqrt{3}=7\sqrt{3}\)
6: \(=\left(5\sqrt{5}-3\sqrt{3}\right)\cdot\dfrac{\sqrt{10}+\sqrt{6}}{16+2\sqrt{15}}\)
\(=\left(\sqrt{5}-\sqrt{3}\right)\cdot\left(8+\sqrt{15}\right)\cdot\dfrac{\left(\sqrt{5}+\sqrt{3}\right)}{8+\sqrt{15}}\)
=5-3
=2
7: \(=\sqrt{2}-\sqrt{7}+\sqrt{7}+\sqrt{2}=2\sqrt{2}\)
