8. The range of $y=\sqrt{x}+\sqrt{1-x}$ is

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8. $[1, \sqrt{2}]$ It is evident that $x \in[0,1]$, let $x=\sin ^{2} \alpha, \alpha \in\left[0, \frac{\pi}{2}\right], y=\sin \alpha+\cos \alpha=\sqrt{2} \sin \left(\alpha+\frac{\pi}{4}\right), \alpha+$ $\frac{\pi}{4} \in\left[\frac{\pi}{4}, \frac{3}{4} \pi\right], y \in[1, \sqrt{2}]$