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Rationalize the denominator of \(\displaystyle \frac{1}{\sqrt[3]{3} - \sqrt[3]{2}}\). With your answer in the form  \(\displaystyle \frac{\sqrt[3]{A} + \sqrt[3]{B} + \sqrt[3]{C}}{D}\)  and the fraction in lowest terms, what is  \(A + B + C + D\)?

 Mar 22, 2023
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The expression simplifies to \(\dfrac{\sqrt[3]{12} + \sqrt[3]{18} + \sqrt[3]{36}}{2}\)

 

Therefore, the answer is 12 + 18 + 36 + 2 = 68.

 Mar 22, 2023

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