Question

Take any three surds and write these surds in descending order.

Answer 1

Consider three surds $\sqrt[12]{5},\sqrt[3]{4}\mathrm{and}\sqrt[4]{6}$.
The orders of $\sqrt[12]{5},\sqrt[3]{4}\mathrm{and}\sqrt[4]{6}$ are 12, 3 and 4.

The LCM of 12 ,3 and 4 is 12.
So, we will make the order of all the surds 12.
$$\begin{gathered} \sqrt[12]{5}, \\ \sqrt[3]{4}=\sqrt[12]{4^4}=\sqrt[12]{256} \\ \mathrm{and}\sqrt[4]{6}=\sqrt[12]{6^3}=\sqrt[12]{216} \end{gathered}$$
Hence, the order is same
Since 256 > 216 >5, $\sqrt[3]{4}>\sqrt[4]{6}>\sqrt[12]{5}$.