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Rationalize the denominator of \(\dfrac{2}{\sqrt[3]{2} + \sqrt[3]{16}}\). The answer can be written in the form of A^(1/3)/B, where A and B are positive integers. Find the minimum possible value of A + B.

 Jun 10, 2022
 #1
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Note that  ∛16 =   ∛2^4  =  2 ∛2

 

So....the denominator just becomes

 

∛2 + 2∛2 =   3∛2

 

 

So    we  have

 

 

  2

___    multiply num / den   by     2^(2/3)  = ∛(2^2) =  ∛4

3∛2

 

2 * ∛ 4                2 * ∛4          2 * ∛4           ∛4             4^(1/3) /  3   

_______  =     _______  =  _______  =   _____ =   

3∛2 * ∛4            3 * ∛8           3 * 2              3

 

A +  B  =   4 + 3   =  7

 

cool cool cool

 Jun 10, 2022

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