Question
Rationalize the denominator of \( \frac{6}{\sqrt[3]{6}} \) \( \frac{6}{\sqrt[3]{6}}=\square \) (Type an exact answer, using radicals as needed.)
Ask by Mills Bond. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{6}{\sqrt[3]{6}} = \sqrt[3]{36} \)
Solution
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Beyond the Answer
To rationalize the denominator of \( \frac{6}{\sqrt[3]{6}} \), we multiply both the numerator and the denominator by \( \sqrt[3]{6^2} \): \[ \frac{6 \cdot \sqrt[3]{6^2}}{\sqrt[3]{6} \cdot \sqrt[3]{6^2}} = \frac{6 \cdot \sqrt[3]{36}}{\sqrt[3]{6^3}} = \frac{6 \cdot \sqrt[3]{36}}{6} = \sqrt[3]{36} \] Thus, the answer is: \[ \frac{6}{\sqrt[3]{6}} = \sqrt[3]{36} \]
