Which irrational number can be added to pi to get a sum that is rational?

The answer is:

The explanation for this exercise is shown below:

1. By definition, a rational number can be written as a fraction, whose numerator and denominator are integers. The irrational numbers can't be written as a fraction.

2. is an irrational number, because you can't write it as a fraction. The only way to get a rational number with the sum of and other irrational number shown in the image attached, is that this number added be , because and is a rational number.