Question

A rational plus an irrational will always be irrational

Answer 1

the answer to this question will be true

Answer 2

That's true.

In fact, suppose that x is irrational, and y is rational. If

`x+y=z`

and z is rational, then you have

`x = z-y`

But
`z-y` is the difference of two rational numbers, and the sum/difference of rational numbers is still a rational number.

This proves that the sum of a rational and an irrational number is still irrational.