Units Digit of a Floor Sum
What is the units digit of the sum
\[
\left\lfloor\sqrt{1}\right\rfloor
+\left\lfloor\sqrt{2}\right\rfloor
+\cdots
+\left\lfloor\sqrt{2025}\right\rfloor\,?
\]
Here, $\lfloor x\rfloor$ denotes the greatest integer less than or equal to $x$.