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Cubes and Cube Roots — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSCubes and Cube Roots2 Marks
Question
Evaluate: $\sqrt[3]{-512}$
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Answer

We know that $\sqrt[3]{-512}=-\sqrt[3]{512}$ Resolving $512$ into prime factors, We get, $512= \underline{2\times2\times 2}\times\underline{2\times2\times2}\times\underline{2\times2\times2}$
$= (2\times2\times2)^3$
$=(8)^3$
$\therefore\sqrt[3]{512}=8$
$\therefore\sqrt[3]{-512}=-\big(\sqrt[3]{512}\big)=-8$

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