Question

Evaluate:
$\sqrt[3]{\frac{729}{1000}}$

Answer 1

$\sqrt[3]{\frac{729}{1000}}$

On factorisation:
$\sqrt[3]{\frac{729}{1000}}$= $\frac{\sqrt[3]{\left(3\times 3\times 3\right)\times \left(3\times 3\times 3\right)}}{\sqrt[3]{\left(2\times 2\times 2\right)\times \left(5\times 5\times 5\right)}}$= $\frac{\sqrt[3]{9\times 9\times 9}}{\sqrt[3]{10\times 10\times 10}}$
$\sqrt[3]{\frac{729}{1000}}$= $\frac{9}{10}$