9:
\(=\sqrt{\sqrt{3}+1-\sqrt{6-2\sqrt{5+2\sqrt{3}-1}}}\)
\(=\sqrt{\sqrt{3}+1-\sqrt{6-2\sqrt{4+2\sqrt{3}}}}\)
\(=\sqrt{\sqrt{3}+1-\sqrt{6-2\left(\sqrt{3}+1\right)}}\)
\(=\sqrt{\sqrt{3}+1-\sqrt{6-2\sqrt{3}-2}}\)
\(=\sqrt{\sqrt{3}+1-\sqrt{4-2\sqrt{3}}}\)
\(=\sqrt{\sqrt{3}+1-\sqrt{3}+1}=\sqrt{2}\)
10:
\(=\sqrt{2010+\sqrt{5}-\sqrt{3-\sqrt{20-2\cdot2\sqrt{5}\cdot3+9}}}\)
\(=\sqrt{2010+\sqrt{5}-\sqrt{3-2\sqrt{5}+3}}\)
\(=\sqrt{2010+\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)
\(=\sqrt{2010+\sqrt{5}-\sqrt{5}-1}=\sqrt{2009}\)
11:
\(=\sqrt{7-2\sqrt{2+5\sqrt{2}+4-\sqrt{2}}}\)
\(=\sqrt{7-2\sqrt{6+4\sqrt{2}}}\)
\(=\sqrt{7-2\left(2+\sqrt{2}\right)}=\sqrt{3-2\sqrt{2}}=\sqrt{2}-1\)
14: \(=\sqrt{6+2\sqrt{5}-\sqrt{20-2\cdot2\sqrt{5}\cdot3+9}}\)
\(=\sqrt{6+2\sqrt{5}-2\sqrt{5}+3}=\sqrt{9}=3\)
