1.92 The value of the algebraic expression $\frac{3 \sqrt{\sqrt{7+\sqrt{48}}}}{2(\sqrt{2}+\sqrt{6})}$ is
(A) $\frac{3}{4}$.
(B) 1 .
(C) $\frac{3 \sqrt{2}}{4}$.
(D) $\frac{9}{16}$.
(E) $\frac{\sqrt{3}}{2}$.
(Chinese Junior High School Mathematics Competition, Xuzhou, Jiangsu Province, 1985)
\[
\begin{aligned}
\text { Original expression } & =\frac{3 \sqrt{\sqrt{7+4 \sqrt{3}}}}{2 \sqrt{2}(1+\sqrt{3})}=\frac{3 \sqrt{2+\sqrt{3}}}{2 \sqrt{2}(1+\sqrt{3})} \\
& =\frac{3}{2 \sqrt{2}} \sqrt{\frac{2+\sqrt{3}}{(1+\sqrt{3})^{2}}}=\frac{3}{2 \sqrt{2}} \cdot \sqrt{\frac{1}{2}} \\
& =\frac{3}{4} .
\end{aligned}
\]

Therefore, the correct choice is (A).