![\boxed{5 \cdot \sqrt{2} \cdot \sqrt[6]{5} }](/tpl/images/0725/3329/79f75.png)
![\sqrt[3]{250} \cdot \sqrt{\sqrt[3]{10} }](/tpl/images/0725/3329/b7f97.png)
![\sqrt{\sqrt[3]{10} } \implies (10^\frac{1}{3} )^\frac{1}{2} =10^\frac{1}{6} =\sqrt[6]{10}](/tpl/images/0725/3329/b65e2.png)
![\therefore \sqrt{\sqrt[3]{10} }=\sqrt[6]{10}](/tpl/images/0725/3329/08e9d.png)
![\text{Solving }\sqrt[3]{250} \cdot \sqrt{\sqrt[3]{10} }](/tpl/images/0725/3329/0eda7.png)
![\sqrt[3]{250}=\sqrt[3]{2\cdot 5^3}=5 \sqrt[3]{2}](/tpl/images/0725/3329/441fd.png)
![\sqrt[6]{2} \cdot \sqrt[6]{5} = \sqrt[6]{10}](/tpl/images/0725/3329/c2f9a.png)
![5 \sqrt[3]{2} \cdot \sqrt[6]{2} \cdot \sqrt[6]{5}](/tpl/images/0725/3329/a7901.png)
![\sqrt[3]{2} \cdot \sqrt[6]{2} = 2^{\frac{1}{3}} \cdot 2^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} }=\sqrt{2}](/tpl/images/0725/3329/76d8b.png)
![5 \sqrt[3]{2} \cdot \sqrt[6]{2} \cdot \sqrt[6]{5} = 5 \cdot \sqrt{2} \cdot \sqrt[6]{5}](/tpl/images/0725/3329/935a1.png)
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