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# Algebra

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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

#1
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Find the minimum possible value of A + B.

Hello Guest!

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

$$A+B=9+4=13$$

!

Jan 10, 2022