1. Four numbers
$$
\begin{array}{l}
\sqrt{2-\sqrt{3}} \cdot \sqrt{2-\sqrt{2-\sqrt{3}}}, \\
\sqrt{2-\sqrt{2-\sqrt{2-\sqrt{3}}}} \sqrt{2+\sqrt{2-\sqrt{2-\sqrt{3}}}}
\end{array}
$$

The product of these is ( ).
(A) $2+\sqrt{3}$
(B) 2
(C) 1
(D) $2-\sqrt{3}$
- 1. C.
$$
\begin{array}{l}
\sqrt{2-\sqrt{3}} \times \sqrt{2-\sqrt{2-\sqrt{3}}} \times \sqrt{2-\sqrt{2-\sqrt{2-\sqrt{3}}}} \times \\
\sqrt{2+\sqrt{2-\sqrt{2-\sqrt{3}}}} \\
=\sqrt{2-\sqrt{3}} \times \sqrt{2-\sqrt{2-\sqrt{3}}} \times \\
\sqrt{2^{2}-(\sqrt{2-\sqrt{2-\sqrt{3}}})^{2}} \\
=\sqrt{2-\sqrt{3}} \times \sqrt{2-\sqrt{2-\sqrt{3}}} \times \\
\sqrt{2+\sqrt{2-\sqrt{3}}} \\
=\sqrt{2-\sqrt{3}} \times \sqrt{2^{2}-(\sqrt{2-\sqrt{3}})^{2}} \\
=\sqrt{2-\sqrt{3}} \times \sqrt{2+\sqrt{3}}=\sqrt{4-3}=1 \text {. } \\
\end{array}
$$