15. Find the smallest positive integer $n$ such that
$$
\sqrt{5 n}-\sqrt{5 n-4}<0.01
$$
15. Answer: 8001
Note that $\sqrt{5 n}-\sqrt{5 n-4}400 \text {. }
$$

If $n=8000$, then $\sqrt{5 n}+\sqrt{5 n-4}=\sqrt{40000}+\sqrt{39996}400$.
So the answer is 8001 .