How I can use the mean value theorem in this problem? Use the Mean Value Theorem to estimate the value of $\sqrt{80}$.
and 
how should we take $f(x)$?
Thanks in advance.
Regards

You want to estimate a value of $f(x) = \sqrt{x}$, so that's a decent place to start. The mean value theorem says that there's an $a \in (80, 81)$ such that
$$
\frac{f(81) - f(80)}{81 - 80} = f'(a).
$$
I don't know what $a$ is, but you know $f(81)$ and you hopefully know how to write down $f'$. How small can $f'(a)$ be?
