Example 14. Find the number of integer solutions $(x, y, z)$ that satisfy $0<x<y<z$, and $\sqrt{1984}=\sqrt{ } x+\sqrt{ } y+\sqrt{ } z$.
$$
\text { Stele } \begin{aligned}
& \sqrt{1984}=8 \sqrt{31} \\
& =\sqrt{31}+2 \sqrt{31}+5 \sqrt{31} \\
& =\sqrt{31}+\sqrt{2} \times 31+\sqrt{5} \times 31 \\
& =\sqrt{31}+3 \sqrt{31}+4 \sqrt{31} \\
& =\sqrt{31}+\sqrt{3} \times 31+\sqrt{2} \times 1 .
\end{aligned}
$$

There are two kinds of correct statements in total.
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