3. Let non-negative real numbers $x, y, z$ satisfy $x+y+z=1$. Then
$$
t=\sqrt{9+x^{2}}+\sqrt{4+y^{2}}+\sqrt{1+z^{2}}
$$

the minimum value of $t$ is $\qquad$.
3. $\sqrt{37}$.

First, $\sqrt{4+y^{2}}+\sqrt{1+z^{2}} \geqslant \sqrt{9+(y+z)^{2}}$.
Then $t \geqslant \sqrt{9+x^{2}}+\sqrt{9+(y+z)^{2}}$
$$
\geqslant 2 \sqrt{9+\frac{1}{4}}=\sqrt{37} \text {. }
$$

When and only when $z=\frac{1}{2} y=\frac{1}{3} x=\frac{1}{6}$, $t_{\text {min }}=\sqrt{37}$.