Solution
= Solution
The continued-fraction algorithm starts with $a_0=3$. Rationalizing the successive remainders gives
$$
\frac1{\sqrt{11}-3}=\frac{\sqrt{11}+3}{2}
=3+\frac1{\sqrt{11}+3},
$$
and
$$
\sqrt{11}+3=6+(\sqrt{11}-3).
$$
The same remainder has returned, so the digits $3,6$ repeat. Therefore
$$
\boxed{\sqrt{11}=[3;\overline{3,6}]}.
$$