How to estimate $\mathcal{O}(\sqrt{n!})$ and $\mathcal{O}(\log{n!})$.
So for example $\sqrt{n!} = \sqrt{1}* \sqrt{2}* ....*\sqrt{n} \leq \sqrt{n}^n$ and $\sqrt{n!} \geq \sqrt{1}^n$. I can't find better bounds. So why is $5^{2n} \in \mathcal{O}(\sqrt{n!})$