$33 \cdot 47$ Given $y=\sqrt{11+6 \sqrt{2}}, x$ represents the fractional part of $y$. Then the value of $x^{2}+2 y$ is
(A) 7.
(B) 8.
(C) 9.
(D) 10.
(China Sichuan Province Junior High School Mathematics Competition, 1991)
[Solution] From $y=\sqrt{11+6 \sqrt{2}}=\sqrt{9+6 \sqrt{2}+2}$
$$
\begin{array}{lc} 
& =3+\sqrt{2}, \\
\because & 1<\sqrt{2}<2, \\
\text { then } & x=(3+\sqrt{2})-(3+1)=\sqrt{2}-1, \\
\text { thus } & x^{2}+2 y=(\sqrt{2}-1)^{2}+2(3+\sqrt{2})=9 .
\end{array}
$$

Therefore, the answer is $(C)$.