- #1
- 3,802
- 95
Can such irrationals like [tex]\sqrt{2}, \pi, e[/tex] ever be added/subtracted to another irrational to give a rational result?
This would have to exclude such occurences like: [tex]\sqrt{2}+(1-\sqrt{2})[/tex] and less obvious irrationals that - for their irrational parts - can be expressed as the negative of the irrational it is being summed with (or the positive if being subtracted).
I'd like to avoid logarithms, as they can easily give 2 irrationals to become a rational.
This would have to exclude such occurences like: [tex]\sqrt{2}+(1-\sqrt{2})[/tex] and less obvious irrationals that - for their irrational parts - can be expressed as the negative of the irrational it is being summed with (or the positive if being subtracted).
I'd like to avoid logarithms, as they can easily give 2 irrationals to become a rational.