Question

PORVE ROOT 2 IS RATIONAL

Answer 1

Answer:

√2is a irrational number but not an rational

ihope itmay help you

Answer 2

Step-by-step explanation:

Let us assume√2 is rational

If it is rational, then there must exist two integers r and s(s ≠0) such that √2 = r/s.

If r and s have a common factor other that 1.

If we get √2 = a/b, where a and b are co-primes. So, b√2 = a.

Squaring on both sides, we get 2b^2 = a^2.

Therefore, 2 divides a^2.

(by theorem) 2divides a.

We can write a =2c for some integer c.

We get 2b^2 = 4c^2, that is b^2 = 2c^2

=> 2 divides b^2

=> 2 divides b

a and b have 2 has a common factor.

But contradicts that a and b are co-prime.

Our assumption that √2 is rational. So, Our assumption is false.

Therefore, that √2 is irrational.