Question

Prove that 7 by root2 is an irrational

Answer 1

Answer:

Let 7/√2 be rational

therefore 7/√2 =a/b where a and b are Co primes

therefore

7/√2 =a/b

7=a√2/b

7b=a√2

7b/a=√2

Therefore √2 is rational,but it contradicts the fact that √2 is irrational so our suppostion that √2 is rational is wrong.

Hence,7/√2 is irrational.

Or for simple way........

We know that 7 is rational and √2 is irrational and when a rational number is divided by an irrational number the quotient obtained would also be irrational.

Hence,7/√2 is irrational.