Question

let X and Y be rational and irrational numbers respectively .Is X + Y necessarily an irrational number give an example in support of your answer.

Answer 1

let x=1/2
and y=√2
so,x+y = 1/2+√2
= (1+2√2)/2 is a rational number but,it contradicts the fact that √2 is irrational so (1+2√2)/2 is irrational.

Answer 2

I hope it's helps you