Question

Find the value of $2\sqrt[3]{33}\times 3\sqrt[3]{34}\times 4\sqrt[3]{32}$.

Answer 1

$2\sqrt[3]{33}\times 3\sqrt[3]{34}\times 4\sqrt[3]{32}$ (same order)
$=(2\times 3\times 4)\times \sqrt[3]{33\times 4\times 2}$ (by using $\sqrt[n]{na}\times \sqrt[n]{nb}\times \sqrt[n]{nc}=\sqrt[n]{nabc}$)
$=24\sqrt[3]{324}=24\sqrt[3]{33\times 2^3}=24\times 2\sqrt[3]{33}=48\sqrt[3]{33}$ .

$\therefore 2\sqrt[3]{33}\times 3\sqrt[3]{34}\times 4\sqrt[3]{32}=48\sqrt[3]{33}$ .