Question

prove that 3+2root2 is irrational ​

Answer 1

Answer:

Let it be a rational no.

i.e. p/q where p and q are co primes and q is not equal to zero.

3+2root2=p/q

2root2=p/q-3

2root2=p-3q/q

root2=p-3q/2q

But root 2 is irrational and p-3q/2q is rational.

This means irrational no. =rational no.

which is never possible.

Thus,it is a contradiction.

Our supposition is wrong.

Hence,3+2root2 is irrational no.