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Rationalize the denominator of \(\frac{3}{\sqrt[3]{3} + \sqrt[3]{81}}\). The answer can be written in the form of \(\frac{\sqrt[3]{A}}{B}\), where A and B are positive integers. Find the minimum possible value of A + B.

 Jan 10, 2022
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Find the minimum possible value of A + B.

 

Hello Guest!

 

\(\frac{3}{\sqrt[3]{3} + \sqrt[3]{81}}= \frac{3}{\sqrt[3]{3} +\sqrt[3]{3}\cdot \sqrt[3]{27}}=\frac{3}{\sqrt[3]{3} (1+3)}\cdot \frac{\sqrt[3]{3}\cdot \sqrt[3]{3}}{\sqrt[3]{3}\cdot \sqrt[3]{3}} =\frac{3\cdot \sqrt[3]{9}}{4\cdot 3}=\color{blue}\frac{ \sqrt[3]{9}}{4}\)

\(A+B=9+4=13\)

laugh  !

 Jan 10, 2022

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