Question

Mark (✓) against the correct answer
$\frac{\sqrt[3]{128}}{\sqrt[3]{250}}=?$
(a) $\frac{3}{5}$
(b) $\frac{4}{5}$
(c) $\frac{2}{5}$
(d) none of these

Answer 1

(b) $\frac{4}{5}$

Resolving the numerator and the denominator into prime factors:

$$\begin{gathered} \frac{\sqrt[3]{128}}{\sqrt[3]{250}}=\sqrt[3]{\frac{128}{250}}=\sqrt[3]{\frac{2\times 8\times 8}{2\times 5\times 5\times 5}}=\sqrt[3]{\frac{\cancel{2}\times 8\times 8}{\cancel{2}\times 5\times 5\times 5}}=\sqrt[3]{\frac{8\times 8}{5\times 5\times 5}} \\ =\sqrt[3]{\frac{{\left(2\right)}^3\times {\left(2\right)}^3}{{\left(5\right)}^3}}=\frac{2\times 2}{5}=\frac{4}{5} \end{gathered}$$