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If $A$, $B$ and $C$ are positive integers such that $\frac{A\sqrt{B}}{C} = \frac{8}{3\sqrt{2}}$, what is the value of $A+B+C$ given that $A$ and $C$ have no common prime factors, and $B$ has no perfect-square factors other than 1?

Guest Jan 12, 2018
 #1
avatar+87301 
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\($\frac{A\sqrt{B}}{C} = \frac{8}{3\sqrt{2}}$\)

 

Implies  that 

 

A√B / C  =  8 / √18         cross-muliply

 

A√[18B] =  8C     ..... let  B  = 2.....and we have

 

A√36  =  8C

 

6A  =  8C       ......this is equalized when  A = 4  and C  = 3

 

Check :

 

4√2 / 3  =  8 / [ 3 √2]

 

4 √2   =  8 / √2

 

√2 * √2  =   8 / 4

 

2  =  2      

 

So     A  +  B   +  C    =      4  +  3  +  2   =      9

 

 

cool cool cool

CPhill  Jan 12, 2018

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