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Cubes and Cube Roots — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSCubes and Cube Roots3 Marks
Question
Evaluate $\sqrt[3]{\frac{-64}{125}}$
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Answer

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

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