Which option gives the correct rational form used in the proof of (\sqrt{3})?

Correct answer: (\sqrt{3}=\frac{p}{q}), where (p,q) are coprime and (q\neq0)

The correct answer is option B: sqrt{3}=p/q, where p and q are coprime integers and q≠0. To prove irrationality by contradiction, assume that sqrt{3} is rational. Every rational number can be expressed as a fraction of integers in lowest terms, so write sqrt{3}=p/q with q nonzero and with no common factor between p and q. Option B states exactly these conditions. Option A is impossible because division by zero is undefined. Option C is not the standard rational form and does not provide a denominator or the needed coprime condition. Option D is merely an expression involving p and does not represent the required general rational number. The lowest-terms condition is important because the proof later shows that both p and q are divisible by 3, creating a contradiction. Memory cue: rational assumption means ‘integer over nonzero integer, reduced fully’.