Question

(vii) $\sqrt[3]{6},\sqrt[4]{8}$

Answer 1

The orders of $\sqrt[3]{6}\mathrm{and}\sqrt[4]{8}$ are 3 and 4.
The LCM of 3 and 4 is 12.
So, we will make the orders of both the surds 12.
$$\begin{gathered} \sqrt[3]{6}=\sqrt[12]{6^4}=\sqrt[12]{1296} \\ \mathrm{and}\sqrt[4]{8}=\sqrt[12]{8^3}=\sqrt[12]{512} \end{gathered}$$
Hence, the order is same.
Since 1296 > 512, $\sqrt[3]{6}>\sqrt[4]{8}$.