Question

prove that root 11 is irrational​

Answer 1

Let √11 be rational. Then

√11 = p/q, where p and q are integers, q≠0 and p and q are co-primes.

Squaring both sides,

(√11)² = (p/q)²

11 = p²/q²

p² = 11q²

This means that p is a multiple of 11.

Let 11a = p

⇒ 121a² = 11q²

⇒ 11a² = q²

This means q is also a multiple of 11.

p and q both are multiples of 11. This means that they are not co-primes.

So, our supposition is wrong. Thus, √11 is irrational.