9. (10 points) A four-digit number, which itself is a perfect square, is composed of two two-digit numbers, both of which are also perfect squares. What is this four-digit number?

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【Analysis】We can first assume this four-digit number to be $\overline{a b c d}$, split it into two halves, the first two digits and the last two digits, and then according to the properties of perfect squares, we can narrow down the range within two-digit numbers, and finally determine these two two-digit numbers respectively.
【Solution】Solution: According to the analysis, let this four-digit number be $\overline{\mathrm{abcd}}=n^{2}, \because$ the first two digits $\overline{\mathrm{ab}}$ are a perfect square, so $\overline{\mathrm{ab}} \geqslant$ 16, $\therefore n \geqslant 41$, and $\because \overline{\mathrm{abcd}}, \overline{\mathrm{ab}}$ are both perfect squares, $\therefore$ the last two digits $\overline{c d} \geqslant 2 n-1 \geqslant 2 \times 41-1=81$, $\therefore \overline{c d}=81, \overline{a b}=16$, this four-digit number is 1681, so the answer is: 1681.