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The ratio of the areas of two squares is \(32/65\). After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form $\frac{a\sqrt{b}}{c}$ where $a$, $b$, and $c$ are integers. What is the value of the sum $a+b+c$?

 Apr 30, 2022
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\($\frac{a\sqrt{b}}{c}$ \)

 

 

The  ratio of their side lengths  =   

 

sqrt (32)  / sqrt (65)  =  

 

sqrt (32) sqrt (65) /  65  = 

 

4sqrt (2)  * sqrt ( 65)  / 65    =

 

4sqrt (130)   / 65

 

a + b + c  = 

 

4 + 130 + 65   =

 

199

 

 

cool cool cool

 Apr 30, 2022

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