已知各项为正数的等比数列 $\left\{a_{n}\right\}$ 中, $a_{1} a_{2} a_{3}=5, a_{7} a_{8} a_{9}=10$, 则 $a_{4} a_{5} a_{6}$ 等于( )
解析 $\because a_{1} a_{2} a_{3}=a_{2}^{3}=5, \therefore a_{2}=\sqrt[3]{5}$.

$\because a_{7} a_{8} a_{9}=a_{8}^{3}=10, \quad \therefore a_{8}=\sqrt[3]{10}$.

$\therefore a_{5}^{2}=a_{2} a_{8}=\sqrt[3]{50}=50 \frac{1}{3}$,

又 $\because$ 数列 $\left\{a_{n}\right\}$ 各项为正数,

$\therefore a_{5}=50 \frac{1}{6}$.

$\therefore a_{4} a_{5} a_{6}=a_{5}^{3}=50 \frac{1}{2}=5 \sqrt{2}$.