Let assume that 4 - 5√2 is rational
Therefore it can be expressed in the form of \(\frac{p}{q}\), where p and q are integers and q ≠ 0
Therefore we can write = 4 - 5√2 = \(\frac{p}{q}\)
5√2 = \(\frac{p}{q}\) - 4
\(\frac{p-4q}{5q}\)is a rational number as p and q are integers.
This contradicts the fact that √2 is irrational, so our assumption is incorrect.
Therefore 4 - 5√2 is irrational.
