Well, let’s try √2 - 1/2
So let’s see if √2 - 1/2 = rational number . We can rewrite that as
√2 = rational number + 1/2
But we have the same problem as before. An irrational number can’t be equal to a rational number. So that means √2 - 1/2 is irrational, too.
What if we tried √2 + 2 ?
Well, we can say √2 + 2 = rational number or √2 = rational number − 2 .
That doesn’t work either. √2 + 2 has to be irrational.
So therefore sum of an irrational and a rational number must be irrational.
