1:
\(=\sqrt{9-2\cdot3\cdot\sqrt{2}+2}-\sqrt{9+2\cdot3\cdot\sqrt{2}+2}\)
\(=3-\sqrt{2}-3-\sqrt{2}=-2\sqrt{2}\)
2: \(=\left|2-\sqrt{5}\right|+\sqrt{9-2\cdot3\cdot\sqrt{5}+5}\)
\(=\sqrt{5}-2+3-\sqrt{5}=1\)
3: \(=\left(2+\sqrt{7}\right)\sqrt{7-2\cdot\sqrt{7}\cdot2+4}\)
\(=\left(\sqrt{7}+2\right)\left(\sqrt{7}-2\right)=7-4=3\)
4:\(=3+\sqrt{2}+\sqrt{4-2\cdot2\sqrt{2}+2}\)
\(=3+\sqrt{2}+2-\sqrt{2}=5\)
5: \(=\sqrt{9-6\sqrt{2}}-\dfrac{\sqrt{6}-\sqrt{2}}{2}+\sqrt{3}-\sqrt{2}-\dfrac{1}{\sqrt{2}}\sqrt{4-2\sqrt{3}}\)
\(=\sqrt{6-2\cdot\sqrt{6}\cdot\sqrt{3}+3}-\dfrac{\sqrt{6}-\sqrt{2}}{2}+\sqrt{3}-\sqrt{2}-\dfrac{1}{\sqrt{2}}\left(\sqrt{3}-1\right)\)
\(=\sqrt{6}-\sqrt{3}-\dfrac{1}{2}\sqrt{6}+\dfrac{1}{2}\sqrt{6}+\sqrt{3}-\sqrt{2}-\sqrt{\dfrac{3}{2}}+\dfrac{1}{\sqrt{2}}\)
\(=\sqrt{6}-\sqrt{2}+\dfrac{\sqrt{2}}{2}-\dfrac{\sqrt{6}}{2}\)
\(=\dfrac{1}{2}\sqrt{6}-\dfrac{1}{2}\sqrt{2}\)
