Question

Reduce the surds $\sqrt{\frac{24}{98}}$ and $\sqrt[3]{316}$ to the surds of same order

Answer 1

Here the order $2$ and $3$ respectively. Hence their LCM is $6$. We wrie
$\sqrt{\frac{24}{98}}=\frac{2}{7}\sqrt{3}=\frac{2}{7}\sqrt[6]{627}$,
and
$\sqrt[3]{316}=2\sqrt[3]{32}=2\sqrt[6]{64}$.
We see that $\left(2/7\right)\sqrt[6]{627}$ and $2\sqrt[6]{64}$ have the same order, $6$.