3:
\(=\sqrt{6-2\cdot\sqrt{6}\cdot1+1}\)
\(=\sqrt{\left(\sqrt{6}-1\right)^2}=\sqrt{6}-1\)
4: \(=\sqrt{22-2\cdot6\sqrt{2}}\)
\(=\sqrt{22-2\cdot3\sqrt{2}\cdot2}\)
\(=\sqrt{\left(3\sqrt{2}-2\right)^2}=3\sqrt{2}-2\)
5: \(\sqrt{7+4\sqrt{3}}=\sqrt{7+2\cdot2\cdot\sqrt{3}}\)
\(=\sqrt{\left(2+\sqrt{3}\right)^2}=2+\sqrt{3}\)
6: \(=\sqrt{17+2\cdot3\cdot2\sqrt{2}}\)
\(=\sqrt{\left(3+2\sqrt{2}\right)^2}=3+2\sqrt{2}\)
7: \(=\sqrt{3+2\cdot\sqrt{3}\cdot1+1}\)
\(=\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}+1\)
8: \(=\sqrt{17+2\cdot3\cdot2\sqrt{2}}\)
\(=\sqrt{\left(3+2\sqrt{2}\right)^2}=3+2\sqrt{2}\)
9: \(=\sqrt{12-2\cdot3\cdot\sqrt{3}}=\sqrt{\left(3-\sqrt{3}\right)^2}=3-\sqrt{3}\)
10: \(=\sqrt{10-2\cdot\sqrt{6}\cdot2}\)
\(=\sqrt{\left(\sqrt{6}-2\right)^2}=\sqrt{6}-2\)
11: \(=\sqrt{27-2\cdot3\sqrt{3}\cdot1+1}\)
\(=\sqrt{\left(3\sqrt{3}-1\right)^2}=3\sqrt{3}-1\)
12:
\(=\sqrt{10-2\cdot\sqrt{6}\cdot2}\)
\(=\sqrt{\left(\sqrt{6}-2\right)^2}=\sqrt{6}-2\)
