If a student tries to prove irrationality of √2 by writing its decimal value, what is the correct evaluation?

Decimal approximation is not a proof

The correct answer is A. Writing √2 as approximately 1.414 or displaying more decimal digits only gives a numerical approximation. A finite decimal is rational, while an observed non-terminating pattern on a calculator does not by itself prove that no fraction equals the number; calculators also display rounded values. A formal school proof assumes √2 = a/b in lowest terms, squares to obtain a² = 2b², and then shows that both a and b must be even, contradicting their coprime status. Alternatively, a rigorous theorem about decimal expansions may be used, but merely copying digits is insufficient. Options B, C, and D assert conclusions that neither the decimal display nor the irrationality argument logically establishes.

This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.