Question
Evaluate $\sqrt[3]{\frac{-64}{125}}$
✓
Answer
$\sqrt[3]{\frac{-64}{125}}$
By prime factorisation method
$\sqrt[3]{\frac{-64}{125}}$
$=\frac{\sqrt[3]{-64}}{\sqrt[3]{125}}$
$=\frac{\sqrt[3]{(-4)\times(-4)\times(-4)}}{\sqrt[3]{5\times5\times5}}$
$=\frac{\sqrt[3]{(-4)^3}}{\sqrt[3]{(5)^3}}$
$\sqrt[3]{\frac{-64}{125}}=\frac{-4}{5}$
$\therefore\sqrt[3]{\frac{-64}{125}}=\frac{-4}{5}$
By prime factorisation method
$\sqrt[3]{\frac{-64}{125}}$
$=\frac{\sqrt[3]{-64}}{\sqrt[3]{125}}$
$=\frac{\sqrt[3]{(-4)\times(-4)\times(-4)}}{\sqrt[3]{5\times5\times5}}$
$=\frac{\sqrt[3]{(-4)^3}}{\sqrt[3]{(5)^3}}$
$\sqrt[3]{\frac{-64}{125}}=\frac{-4}{5}$
$\therefore\sqrt[3]{\frac{-64}{125}}=\frac{-4}{5}$
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