\(\sqrt{\sqrt{5-\sqrt{3-\sqrt{29-12\sqrt{5}}}}}\)
\(=\sqrt{\sqrt{5-\sqrt{3-\sqrt{\left(2\sqrt{5}\right)^2-2.2\sqrt{5}.3+9}}}}\)
\(=\sqrt{\sqrt{5-\sqrt{3-\sqrt{\left(2\sqrt{5}-3\right)^2}}}}\)
\(=\sqrt{\sqrt{5-\sqrt{3-2\sqrt{5}+3}}}\)
\(=\sqrt{\sqrt{5-\sqrt{5-2\sqrt{5}+1}}}\)
\(=\sqrt{\sqrt{5-\sqrt{\left(\sqrt{5}-1\right)^2}}}\)
\(=\sqrt{\sqrt{5-\sqrt{5}+1}}\)
\(=\sqrt{\sqrt{6-\sqrt{5}}}\)