Question

Let x and y be a rational and irrational number. If x +y is necessarily an irrational number. Give
example in support of your answer.

Answer 1

If possible,let (x+y) be rational. Then,
(x+y) is rational and x is rational.
{(x+y)-x} is rational [because, difference between rational is rational]
y is rational.
This contradicts the fact that y is irrational.
This contradiction arises by assuming (x+y) is rational. 
So, (x+y) is irrational.
For example 2 is a rational number and √3 is an irrational number .
But (2+√3) is irrational.