Prove that there is no rational number whose square is 2 :
Answer: (c) proof by contradiction
√2 = m/n
where n and m are relatively prime, reduced to simplest form.
Clearly then, m cannot be even.
Square both sides:
2 = m² / n²
2 n² = m²
m² is even, so m must also be even.
Therefore assumption is false, and √2 cannot be expressed as a ratio of relatively prime integers so √2 is irrational, whose square is 2.