Which option gives the correct rational form used in the proof of (\sqrt{2})?

Correct answer: (\sqrt{2}=\frac{a}{b}), where (a,b) are coprime and (b\neq0)

The direct answer is Option A: √2 = a/b, where a and b are coprime integers and b ≠ 0. This is the standard form used when assuming a rational number. A rational number can be expressed as a ratio of two integers, and the fraction is taken in lowest terms so that the numerator and denominator have no common factor. The denominator cannot be zero because division by zero is undefined. Option A is correct. Option B is invalid because a/0 has no defined value. Option C, a + b, is a sum of integers, not the required general ratio form; it also does not set up the proof correctly. Option D, 2a, is simply twice an integer and does not represent the necessary rational fraction with a nonzero denominator. After using Option A, squaring leads to a² = 2b² and then to the contradiction that both a and b are even. Memory cue: rational means “integer over integer,” lowest terms, denominator not zero.