10.3. Let $n$ - be a natural number. What digit stands immediately after the decimal point in the decimal representation of the number $\sqrt{n^{2}+n}$?
Answer: 4.

Solution. We will prove that $(n+0.4)^{2} < 0.8$. The last inequality is true for any natural $n$.
2) $n^{2}+n < (n+0.5)^{2} \Leftrightarrow n < n+0.25$, which is obvious.

Evaluation Criteria.

“+” A complete and justified solution is provided

“Ғ” The correct answer is provided, but only one of the two required inequalities is proven

“-” The correct answer is obtained by considering specific examples

“-” Only the answer is provided

“-” The problem is not solved or is solved incorrectly