Question

Reduce $\sqrt[4]{42},\sqrt[3]{33},\sqrt[5]{54^2}$ into surds of the same order.

Answer 1

Given, $\sqrt[4]{42}$, $\sqrt[3]{33}$ and $\sqrt[5]{54^2}$.

To make the order of the surds same, we take $LCM$ of the given orders.

Then, $LCM$ of $4$, $3$ and $5$ is $60$.

$\sqrt[4]{42}=\sqrt[60]{602^{15}}$,

$\sqrt[3]{33}=\sqrt[60]{603^{20}}$,

$\sqrt[5]{54^2}=\sqrt[60]{604^{24}}$.

THe reduced form of the given surds into surds of the same order are, $\sqrt[60]{602^{15}}$, $\sqrt[60]{603^{20}}$ and $\sqrt[60]{604^{24}}$.