Question

Prove that root 2 is irrational. Some simple method will be appreceated

Answer 1

let√2 be rational
∴√2 = p/q for co - prime integers p and q where q ≠0
2 = p²/q²
2q² = p²
therefore p² is divisible by 2
∴p is divisible by 2
∴ p = 2c for some integer c
substituting it in 2q² = p²
2q² = 4c²
2c² = q²
∴q² is divisible by 2
∴q is divisible by 2
∴both p and q are divisible by 2
but this is not possible as p and q are co-prime
this contradiction has arisen from our assumption that √2 is rational
∴√2 is irrational