11. Find the greatest integer less than $(2+\sqrt{3})^{4}$.
11. Ans: 193
$$
\begin{aligned}
(2+\sqrt{3})^{4} & =\left[(2+\sqrt{3})^{2}\right]^{2}=(4+4 \sqrt{3}+3)^{2} \\
& =(7+4 \sqrt{3})^{2}=49+56 \sqrt{3}+48 \approx 193.9
\end{aligned}
$$

Thus, the greatest integer less than $(2+\sqrt{3})^{4}$ is 193 .