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 $a+b+c$?
I'm not Chris, but I can help you with this
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: √16⋅√2⟹4√2.
We can use this same thing to find the square root of 63.
√63⟹√9⋅√7⟹3√7
So when finding the square roots, our fraction becomes √32√63, which using our steps makes the fraction 4√23√7
To rationalize this, we need to multiply √7 on both sides, so this gives us:
4√2⋅√73√7⋅√7⟹4√1421
That makes a=4, b=14, and c=21. Adding 4+14+21 give us 39