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Section 1.3 : Radicals

6. Evaluate : \(\sqrt[3]{{ - 512}}\)

Hint : Recall that the easiest way to evaluate radicals is to convert to exponential form and then also recall that we evaluated exponential forms in the Rational Exponent section.
Show Solution

All we need to do here is to convert this to exponential form and then recall that we learned how to evaluate the exponential form in the Rational Exponent section.

\[\sqrt[3]{{ - 512}} = {\left( { - 512} \right)^{\frac{1}{3}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 8}}\hspace{0.25in}\hspace{0.25in}\hspace{0.25in}{\mbox{because }}\hspace{0.25in}\,\,\,{\left( { - 8} \right)^3} = - 512\]