3. When $a$ and $b$ are both rational numbers, the point $P(a, b)$ is called a rational point. Let $A(\sqrt{1998}, 0), B(0$, $\sqrt{2000})$, then on the line $A B$ ( .
(A) there are no rational points
(B) there is only one rational point
(C) there are only two rational points
(D) there are infinitely many rational points
3. A.

Let the rational point $P(a, b)$ be on the line $AB$, then
$$
\begin{array}{l}
b=-\frac{\sqrt{2000}}{\sqrt{1998}}(a-\sqrt{1998}), \\
b^{2}=\frac{2000}{1998}\left(a^{2}+1998-2 a \sqrt{1998}\right) .
\end{array}
$$

When $a$ is a non-zero rational number, $b^{2}$ is an irrational number, which contradicts the fact that $P(a, b)$ is a rational point.