Using the squeeze theorem $\lim\limits\_{n \rightarrow \infty} (\sqrt[n]{n^2+2n+3}) = 1$:

$\sqrt[n]{3} \le \sqrt[n]{n^2+2n+3} \le \sqrt[n]{n}^2 \cdot \sqrt[n]{n} \cdot \sqrt[n]{2} \cdot \sqrt[n]{3}$

Now I'd like to see whether I could also use L'Hôpital here, but I can't figure how that'd work.

I've found one similar question with an answer that I don't understand (first one), that may help: [limit of n-th root of polynomial](https://math.stackexchange.com/questions/971788/limit-of-n-th-root-of-polynomial)