2:
\(=\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)
\(=\sqrt{13+30\left(\sqrt{2}+1\right)}\)
\(=\sqrt{43+30\sqrt{2}}\)
\(=\sqrt{25+2\cdot5\cdot3\sqrt{2}+18}\)
\(=5+3\sqrt{2}\)
3:
\(=\sqrt{6+2\sqrt{5-2\sqrt{3}-1}}\)
\(=\sqrt{6+2\left(\sqrt{3}-1\right)}=\sqrt{4+2\sqrt{3}}=\sqrt{3}+1\)
8:
\(=\sqrt{6+2\sqrt{6-2\left(\sqrt{3}+1\right)}}\)
\(=\sqrt{6+2\cdot\sqrt{6-2\sqrt{3}-2}}\)
\(=\sqrt{6+2\left(\sqrt{3}-1\right)}=\sqrt{4+2\sqrt{3}}=\sqrt{3}+1\)
4:
\(=\sqrt{4+\sqrt{5\sqrt{3}+5\left(\sqrt{48-10\left(2+\sqrt{3}\right)}\right)}}\)
\(=\sqrt{4+\sqrt{5\sqrt{3}+5\left(\sqrt{28-10\sqrt{3}}\right)}}\)
\(=\sqrt{4+\sqrt{5\sqrt{3}+5\left(5-\sqrt{3}\right)}}\)
\(=\sqrt{4+5}=3\)
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