Let the side lengths of the two squares be $a$ and $b$.
The area ratio is given by $\frac{a^2}{b^2} = \frac{32}{63}$.
Cross multiplying, we get $63a^2 = 32b^2$.
Taking the square root of both sides, we have $\sqrt{63}a = \sqrt{32}b$.
Rationalizing the denominator, we get $\frac{a}{b} = \frac{\sqrt{32}}{\sqrt{63}} = \frac{4\sqrt{2}}{3\sqrt{7}} = \frac{4\sqrt{2}}{3\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}} = \frac{4\sqrt{14}}{21}$.
Thus, $a+b+c = 4+14+21 = \boxed{39}$.
The answer is: 39
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The area ratio of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed as a simplified fraction in the form of a√b/c, where a, b, and c are integers. Find the value of the sum a + b + c.

### Answer:
