13. Find the smallest integer greater than $(1+\sqrt{2})^{3}$.
13. Ans: 15
$$
(1+\sqrt{2})^{3}=1+3 \sqrt{2}+3 \times 2+2 \sqrt{2}=7+5 \sqrt{2} \text {. }
$$

Observe that $1.4<\sqrt{2}<1.5$. Thus
$$
\begin{array}{l}
7+5 \times 1.4<7+5 \sqrt{2}<7+5 \times 1.5 \\
\Longrightarrow \quad 14<7+5 \sqrt{2}<14.5 \text {. } \\
\end{array}
$$

Therefore, the smallest integer greater than $(1+\sqrt{2})^{3}$ is 15 .