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The ratio of the areas of two squares is $\frac{32}{63}$. 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 $a+b+c$?

 Nov 18, 2020
 #1
avatar+55 
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I'm not Chris, but I can help you with this smiley

 

First, we need to find the square roots of the 2 squares, because the squares of them will give us 32 and 63. So, the square root of 32 is 32, which simplifies to: 16242

 

We can use this same thing to find the square root of 63. 

 

639737

 

So when finding the square roots, our fraction becomes 3263, which using our steps makes the fraction 4237

 

To rationalize this, we need to multiply 7 on both sides, so this gives us: 

 

42737741421

 

That makes a=4, b=14, and c=21. Adding 4+14+21 give us 39

 Nov 18, 2020
 #2
avatar+153 
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You misspelled help.

 

 

 

 

 

 

 

 

 

 

just jokingwink

 Nov 18, 2020

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