31. Given that 2 is both the square root of $x-2$ and the cube root of $2 x-y+1$, then the arithmetic square root of $x^{2}-4 y$ is
Answer: 4
Solution: From the given conditions $\left\{\begin{array}{l}x-2=4 \\ 2 x-y+1=8\end{array}\right.$, we solve to get $\left\{\begin{array}{l}x=6 \\ y=5\end{array}\right.$,
$$
x^{2}-4 y=6^{2}-4 \times 5=16 \text {, }
$$

Therefore, the arithmetic square root of $x^{2}-4 y$ is 4.