HMMT 2025 A2

Mark writes the expression $\sqrt{abcd}$ on the board, where $abcd$ is a four-digit number and $a \neq 0$ . Derek, a toddler, decides to move the $a$ , changing Mark's expression to $a\sqrt{bc}$ . Surprisingly, these two expressions are equal. Compute the only possible four-digit number $abcd$ .