Maharashtra BoardEnglish MediumSTD 8MathsCubes and Cube Roots2 Marks
Question
Evaluate:
$\sqrt[3]{-512}$
✓
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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