Question

Prove that 4-3root2 is irrational

Answer 1

Let 4-3√2 be a rational number.
A rational number can be written in the form of p/q where p,q are integers and q ≠ 0

4-3√2 = p/q
3√2 = 4 - p/q
3√2 = (4q-p)/q
√2 = (4q-p)/3q

p,q are integers then (4q-p)/3q is a rational number.
Then √2 must be a rational number.
But this contradicts the fact that √2 is an irrational number.
So, our supposition is false.
Hence, 4-3√2 is an irrational number.