Find the last three digits of the product of the [positive roots](https://artofproblemsolving.com/wiki/index.php/Positive_root) of
$\sqrt{1995}x^{\log_{1995}x}=x^2$.
Taking the $\log_{1995}$ ([logarithm](https://artofproblemsolving.com/wiki/index.php/Logarithm)) of both sides and then moving to one side yields the [quadratic equation](https://artofproblemsolving.com/wiki/index.php/Quadratic_equation) $2(\log_{1995}x)^2 - 4(\log_{1995}x)  + 1 = 0$. Applying the [quadratic formula](https://artofproblemsolving.com/wiki/index.php/Quadratic_formula) yields that $\log_{1995}x = 1 \pm \frac{\sqrt{2}}{2}$. Thus, the product of the two roots (both of which are positive) is $1995^{1+\sqrt{2}/2} \cdot 1995^{1 - \sqrt{2}/2} = 1995^2$, making the solution $(2000-5)^2 \equiv \boxed{025} \pmod{1000}$.