Question

let x be a rational number and y be an irrational number.Is x+y necessarily an irrational number? Give an example in support of your answer..

Answer 1

Let x be 1 which is a rational number
Let y be $\sqrt{2}$ which is an irrational number

Then x + y = 1 + $\sqrt{2}$ which is an irrational number.

So it verifies that sum of rational number and irrational number is always an irrational number.