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