Question

Write the irrational numbers $\sqrt[3]{32},\sqrt[4]{44},\sqrt{3}$ in (i) ascending order (ii) descending order.

Answer 1

The order of the irrational numbers $\sqrt[3]{32},\sqrt[4]{42}$ and

$\sqrt{3}$ are $3,4$ and $2$ respectively.

LCM of $2,3$ and $4$ is $12$. Now, we convert each irrational number as of order $12$.

$\sqrt[3]{32}=\sqrt[12]{122^4}=\sqrt[12]{1216}$

$\sqrt[4]{44}=\sqrt[12]{124^3}=\sqrt[12]{1264}$

$\sqrt{3}=\sqrt[12]{123^6}=\sqrt[12]{12729}$

$\therefore$ Ascending order: $\sqrt[3]{32},\sqrt[4]{44},\sqrt{3}$

Descending order: $\sqrt{3},\sqrt[4]{44},\sqrt[3]{32}$.