While assuming (\sqrt{3}) rational, which form is most suitable for proof?

Correct answer: (\sqrt{3}=\frac{u}{v}), where (\gcd(u,v)=1) and (v\neq0)

The direct answer is C: square root of 3 equals u/v, where u and v are coprime integers and v is not zero. To prove irrationality by contradiction, assume the number is rational. By the definition of a rational number, it can be written as a quotient of integers with a nonzero denominator. We may reduce that fraction to lowest form, so gcd(u,v)=1. Squaring gives u squared equals 3v squared. Then 3 divides u squared, so the prime property gives 3 divides u; substitution then gives 3 divides v. This contradicts coprimality. Option A is impossible because division by zero is undefined. Option B is not the required general form; a rational number need not be an integer sum. Option C is correct and contains every needed condition. Option D is too restrictive and does not represent every rational assumption. Memory cue: rational number = coprime integer fraction with nonzero denominator.