8: \(=\sqrt{49-2\cdot5\cdot2\sqrt{6}}+\sqrt{49+2\cdot5\cdot2\sqrt{6}}\)
\(=5-2\sqrt{6}+5+2\sqrt{6}\)
=10
7: \(=\sqrt{17-2\cdot3\cdot2\sqrt{2}}-\sqrt{17+2\cdot3\cdot2\sqrt{2}}\)
\(=3-2\sqrt{2}-3-2\sqrt{2}=-4\sqrt{2}\)
6: \(=\sqrt{13+2\cdot2\sqrt{2}\cdot\sqrt{5}}+\sqrt{13-2\cdot2\sqrt{2}\cdot\sqrt{5}}\)
\(=2\sqrt{2}+\sqrt{5}+2\sqrt{2}-\sqrt{5}=4\sqrt{2}\)
5:
\(=\sqrt{11-2\cdot3\cdot\sqrt{2}}-\sqrt{2-2\cdot\sqrt{2}\cdot1+1}\)
\(=3-\sqrt{2}-\sqrt{2}+1=4-2\sqrt{2}\)
4: \(=\sqrt{3}-\sqrt{2}-\sqrt{3}-\sqrt{2}=-2\sqrt{2}\)
2:
\(=\sqrt{5}-\sqrt{2}-\sqrt{5}-\sqrt{2}=-2\sqrt{2}\)
1:
\(=\sqrt{14-2\cdot3\cdot\sqrt{5}}+\sqrt{14+2\cdot3\cdot\sqrt{5}}\)
\(=3-\sqrt{5}+3+\sqrt{5}=6\)
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