Question

Prove that 6+ V2 is irrational.​

Answer 1

Answer:

Explanation:

assume 6+root2 to be rational number.

therefore it is equal to p/q where q is not equal to 0 and it belongs to integer.

6+root2=p/q,(send 6 to rhs it becomes -6/1)

root2=p/q-6(now take lcm of qand 1, it becomes p-6q/q)

p-6q /q is a rational number therefore root2 is also rational number.

but according to the fact root2 is a irrational number therfore this contradiction has arisen because of our incorrect assumption.

therefore 6+root2 is irrational.