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# geometry question

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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

Apr 30, 2022