Question

Упростить выражение $\sqrt{ \sqrt{5} - \sqrt{3- \sqrt{29-12 \sqrt{5} } } }$

Answer 1

$\sqrt{\sqrt5-\sqrt{3-\sqrt{29-12\sqrt5}}}=\sqrt{\sqrt5-\sqrt{3-\sqrt{(\sqrt{20}-3)^2}}}=\\\\=\sqrt{\sqrt5-\sqrt{3-(\sqrt{20}-3)}}=\sqrt{\sqrt5-\sqrt{6-\sqrt{20}}}=\\\\=\sqrt{\sqrt5-\sqrt{(\sqrt5-1)^2}}=\sqrt{\sqrt5-(\sqrt5-1)}=\sqrt1=1$