Question

$\sqrt[8]{80},\sqrt[4]{40}$

Answer 1

The orders of $\sqrt[8]{80}\mathrm{and}\sqrt[4]{40}$ are 8 and 4.
The LCM of 8 and 4 is 8.
So, we will make the order of both the surds 8.
$$\begin{gathered} \sqrt[8]{80} \\ \mathrm{and}\sqrt[4]{40}=\sqrt[8]{{40}^2}=\sqrt[8]{1600} \end{gathered}$$

Hence, the order is same.
Since 80 < 1600, $\sqrt[8]{80}<\sqrt[4]{40}$.