Question

Evaluate $\sqrt[3]{216\times 343}.$

Answer 1

$\sqrt[3]{216\times 343}$
By prime factorisation:

$\sqrt[3]{216\times 343}$ = $\sqrt[3]{216}\times \sqrt[3]{343}=\sqrt[3]{2\times 2\times 2\times 3\times 3\times 3}\times \sqrt[3]{7\times 7\times 7}=\sqrt[3]{{\left(2\right)}^3\times {\left(3\right)}^3}\times \sqrt[3]{{\left(7\right)}^3}$
$\sqrt[3]{216\times 343}$ = $\left(2\right)\times \left(3\right)\times \left(7\right)=42$

∴ $\sqrt[3]{216\times 343}$ = $42$