8 Let $x \in \mathbf{R}$, then the minimum value of the function $f(x)=\sqrt{x^{2}+1}+\sqrt{(x-12)^{2}+16}$ is $\qquad$
(8) As shown in the figure, take $A$ as the origin on the number line, $A B=12$, then construct perpendicular lines $A C$ and $B D$ such that $A C=1, B D=4$. On the number line, take point $P$ such that $A P=x$, then
$$
f(x)=|C P|+|D P|,
$$

When $C, P, D$ are collinear, the value of $f$ is minimized, at this time
$$
f_{\min }=|C D|=|A E|=\sqrt{12^{2}+5^{2}}=13
$$