\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-6\sqrt{20}}}}\)=\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{20-2.\sqrt{20}.3+9}}}\)=\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(\sqrt{20}-3\right)^2}}}\)
=\(\sqrt{\sqrt{5}-\sqrt{3-\left|\sqrt{20}-3\right|}}\)=\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{20}+3}}\)=\(\sqrt{\sqrt{5}-\sqrt{6-\sqrt{20}}}\)=\(\sqrt{\sqrt{5}-\sqrt{5-2\sqrt{5}.1+1}}\)
=\(\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}\)=\(\sqrt{\sqrt{5}-\left|\sqrt{5}-1\right|}\)=\(\sqrt{\sqrt{5}-\sqrt{5}+1}\)=\(\sqrt{1}\)=1
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