Question

Find two irrational numbers whose sum is rational

Answer 1

Two irrational numbers such that when you add them gives you a rational number could be
`√(5)` and
`-√(5)-2`.

The result when adding these is -2 which is a rational number.

(There are infinitely many examples.)

Explanation:

How about opposite irrational numbers?

The sum of opposite numbers, no matter the classification of that number, is 0.

So examples:

`2√(3)+-2√(3)=0`

`\pi+(-\pi)=0`

`-√(2)+√(2)=0`

If you wanted some more examples that have a sum other than 0:

`(√(3))+(-√(3)+1)=1`

`(\pi-1)+(-\pi+4)=3`

There are infinite amount of examples of the sum of two irrational numbers being a rational.

My last example: Two irrational numbers such that when you add them gives you a rational number could be
`√(5)` and
`-√(5)-2`.

The result when adding these is -2 which is a rational number.