+0

+4
78
5
+294

Rationalize the denominator of $$\frac{2}{\sqrt[3]{4}+\sqrt[3]{32}}$$. 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 $$A+B$$.

Feb 21, 2021

#1
+118069
+2

∛32  =   ∛4  *  ∛8  =   ∛4  *  2

So  we  have

2

__________     =

∛4  +  ∛32

2

__________    =

∛4  + 2 ∛4

2

___________   =

∛4  ( 1 + 2)

2

____________                  multiply  top / bottom  by      ∛2

3  ∛4

2  ∛2

_____________    =

3  ∛4 *  ∛2

2 ∛2

________   =

3 *  ∛8

2  ∛2

________   =

3  *  2

∛2

____             A  +  B  =    5       CORRECTED  !!!!

3

Feb 21, 2021
edited by CPhill  Feb 21, 2021
#2
+294
+3

Thank you!

calvinbun  Feb 21, 2021
#3
+294
+3

It's wrong though...

calvinbun  Feb 21, 2021
#4
+118069
+1

OOPs....just  a small error

Should  be       ∛2 /  3

A + B =   5

Sorry!!!!

Feb 21, 2021
edited by CPhill  Feb 21, 2021
edited by CPhill  Feb 21, 2021
#5
+294
+3

Thank you!

calvinbun  Feb 22, 2021