Đáp án:
$\begin{array}{l}
\mathop {\lim }\limits_{n \to {0^ + }} \frac{{\sqrt {{n^2} + n} - \sqrt n }}{{{n^2}}}\\
= \mathop {\lim }\limits_{n \to {0^ + }} \frac{{{n^2} + n - n}}{{{n^2}\left( {\sqrt {{n^2} + n} + \sqrt n } \right)}}\\
= \mathop {\lim }\limits_{n \to {0^ + }} \frac{1}{{\sqrt {{n^2} + n} + \sqrt n }}\\
= + \infty
\end{array}$