2. The sum of the maximum and minimum values of the algebraic expression $\sqrt{t-2}+\sqrt{4-t}$ is equal to

保留了源文本的换行和格式。
$2.2+\sqrt{2}$.
Let $y=\sqrt{t-2}+\sqrt{4-t}$.
Obviously, $y \geqslant 0, 2 \leqslant t \leqslant 4$.
$$
\begin{array}{l}
\text { Then } y^{2}=2+2 \sqrt{-(t-3)^{2}+1} \\
\Rightarrow 2 \leqslant y^{2} \leqslant 4 \Rightarrow \sqrt{2} \leqslant y \leqslant 2 \\
\Rightarrow y_{\text {max }}+y_{\text {min }}=2+\sqrt{2} .
\end{array}
$$