3:
d: \(\sqrt{23-6\sqrt{10+4\sqrt{3-2\sqrt{2}}}}\)
\(=\sqrt{23-6\sqrt{10+4\left(\sqrt{2}-1\right)}}\)
\(=\sqrt{23-6\sqrt{6+4\sqrt{2}}}\)
\(=\sqrt{23-6\left(2+\sqrt{2}\right)}\)
\(=\sqrt{11-6\sqrt{2}}=3-\sqrt{2}\)
e: \(A=\sqrt{\sqrt{2}+2\sqrt{3}+\sqrt{18-8\sqrt{2}}}\)
\(=\sqrt{\sqrt{2}+2\sqrt{3}+4-\sqrt{2}}\)
\(=\sqrt{4+2\sqrt{3}}=\sqrt{3}+1\)
f: \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
\(=\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)
\(=\sqrt{13+30\left(\sqrt{2}+1\right)}=\sqrt{43+30\sqrt{2}}\)
\(=\sqrt{25+2\cdot5\cdot3\sqrt{2}+18}\)
\(=5+3\sqrt{2}\)
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