Why is finding the decimal value not necessary in the proof of (\sqrt{2})?

Correct answer: Because the proof is based on divisibility and contradiction

The direct answer is option B. The proof of √2 is not a numerical approximation exercise; it is a proof about whether a number can be written as a ratio of integers. Assume, for contradiction, that √2 = p/q, where p and q are integers with no common factor and q is nonzero. Squaring gives p² = 2q². Hence p² is even, so p is even; write p = 2k. Substitution gives 4k² = 2q², so q² = 2k², and q is also even. Thus p and q have a common factor 2, contradicting their lowest-term condition. Option B is correct because divisibility, parity and contradiction do the work. Option A is false: √2 is not zero. Option C is false because √2 is not an integer. Option D is false because the proof does use the fraction p/q. Decimal approximations may illustrate the value, but they are not needed for this logical proof.