Let us assume that (4 – 5√2 ) is a rational.
Subtract given number form 4, considering 4 is a rational number.
As we know, Difference of two rational numbers is a rational.
4 – (4 – 5√2 ) is rational
5√2 is rational
Which is only possible if 5 is rational and √2 is rational
As we know, product of two rational number is rational.
But the fact is √2 is an irrational.
Which is contradict to our assumption.
Hence, 4 – 5√2 is irrational. Hence Proved.
