3. Given the function
$$
y=\sqrt{\left(x^{2}-2\right)^{2}+(x-5)^{2}}+\sqrt{\left(x^{2}-3\right)^{2}+x^{2}} \text {. }
$$

Then the minimum value of the function is $\qquad$
3. $\sqrt{26}$.

The function $y$ can be regarded as the sum of the distances from point $P\left(x, x^{2}\right)$ on the parabola $y=x^{2}$ to points $M(5,2)$ and $N(0,3)$.

From the graph, it is easy to see that when point $P$ is the intersection of segment $M N$ and the parabola, $y$ is minimized, at which time,
$$
y_{\text {min }}=|M N|=\sqrt{26} .
$$