7. Let $u, v, w$ be positive real numbers, satisfying the condition $u \sqrt{v w}+v \sqrt{w u}+w \sqrt{u v}=1$. Find the minimum value of $u+v+w$. (3rd China Girls Mathematical Olympiad Problem)
$$\text { 7. } \begin{aligned}
1= & u \sqrt{v w}+v \sqrt{w u}+w \sqrt{u v}=\sqrt{u v w}(\sqrt{u}+\sqrt{v}+\sqrt{w})= \\
& \sqrt{3 u v w} \sqrt{\frac{(\sqrt{u}+\sqrt{v}+\sqrt{w})^{2}}{3}} \leqslant \\
& \sqrt{3\left(\frac{u+v+w}{3}\right)^{3}} \sqrt{u+v+w}= \\
& \frac{1}{3}(u+v+w)^{2}
\end{aligned}$$

Therefore, the minimum value of $u+v+w$ is $\sqrt{3}$.