9. Arrange the sequence of numbers
$$
\sqrt{2}, 2, \sqrt{6}, 2 \sqrt{2}, \sqrt{10}, \cdots, 10 \sqrt{2}
$$

in the following manner:
\begin{tabular}{ccccc}
$\sqrt{2}$ & 2 & $\sqrt{6}$ & $2 \sqrt{2}$ & $\sqrt{10}$ \\
$2 \sqrt{3}$ & $\sqrt{14}$ & 4 & $3 \sqrt{2}$ & $2 \sqrt{5}$ \\
$\sqrt{22}$ & $2 \sqrt{6}$ & $\cdots$ & $\cdots$ & $\cdots$ \\
$\vdots$ & & & & $\vdots$ \\
$\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $10 \sqrt{2}$
\end{tabular}

According to this arrangement, the position of $3 \sqrt{2}$ can be denoted as $(2, 4)$, and the position of $2 \sqrt{6}$ can be denoted as $(3, 2)$. Therefore, the position of the largest rational number in this sequence, according to this arrangement, can be denoted as
9. $(20,3)$.

The sequence is arranged according to the square roots of even numbers, $\sqrt{2}, \sqrt{4}, \sqrt{6}, \cdots$, $\sqrt{200}$, totaling 100. Each row contains 5 numbers, making 20 rows in total, with the largest rational number being $\sqrt{196}=14$.