$$
\begin{array}{l}
\text { 1. } \sqrt{5-\sqrt{5}-\sqrt{3-\sqrt{29-12 \sqrt{5}}}} \text { and } \\
\sqrt{3-\sqrt{29-12 \sqrt{5}} \text { have a ( ). }}
\end{array}
$$
1. $\sqrt{5-\sqrt{5}-\sqrt{3-\sqrt{29-12 \sqrt{5}}}}$ and
(A) sum of 1
(B) difference of 1
(C) product of 1
(D) quotient of 1

- 1.D.

Since $\sqrt{29-12 \sqrt{5}}=\sqrt{(3-2 \sqrt{5})^{2}}=2 \sqrt{5}-3$, then
$$
\begin{array}{l}
\sqrt{3-\sqrt{29-12 \sqrt{5}}}=\sqrt{3-(2 \sqrt{5}-3)} \\
=\sqrt{6-2 \sqrt{5}}=\sqrt{(\sqrt{5}-1)^{2}}=\sqrt{5}-1
\end{array}
$$

And $\sqrt{5-\sqrt{5}-\sqrt{3-\sqrt{29-12 \sqrt{5}}}}$
$$
=\sqrt{5-\sqrt{5}-(\sqrt{5}-1)}=\sqrt{6-2 \sqrt{5}}=\sqrt{5}-1 \text {. }
$$

Therefore, the quotient of the two is 1.