$\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}$
=$\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-6\sqrt{20}}}}$
=$\sqrt{\sqrt{5}-\sqrt{3-\sqrt{20-2.\sqrt{20}.3+9}}}$
=$\sqrt{\sqrt{5}-\sqrt{3-\sqrt{(\sqrt{20}-3)^2}}}$
=$\sqrt{\sqrt{5}-\sqrt{3-(\sqrt{20}-3)}}$
=$\sqrt{\sqrt{5}-\sqrt{6-\sqrt{20}}}$
=$\sqrt{\sqrt{5}-\sqrt{5-2.1.\sqrt{5}+1}}$
=$\sqrt{\sqrt{5}-\sqrt{(\sqrt{5}-1)^2}}$
=$\sqrt{\sqrt{5}-(\sqrt{5}-1)}$
=$\sqrt{1}$
=1
