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I was solving some questions on Math Stack Exchange about irrational numbers when suddenly this question struck me.

We know that $e$ is irrational and that $\pi$ is also irrational.

Then is $\pi\cdot e$ rational or irrational?

projectilemotion
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Marble
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  • Thats hat ia m asking – Marble Oct 04 '16 at 02:40
  • @suomynonA we need to be a little careful since product of two irrationals can be rational. – Jacky Chong Oct 04 '16 at 02:42
  • When is $\pi^e$ rational? Isn't it always irrational? – suomynonA Oct 04 '16 at 02:43
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    Nobody knows! (But it's likely to be irrational) – arkeet Oct 04 '16 at 02:44
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    Its an open problem https://en.wikipedia.org/wiki/Irrational_number#Open_questions –  Oct 04 '16 at 02:46
  • That is the reason behind down votes?? – Marble Oct 04 '16 at 02:50
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    I didn't downvote, but I'd wager those who did believe this question doesn't have sufficient context and doesn't show sufficient effort. "Bare" questions like this one that just ask for information without any context as to why you're asking or some reasoning toward an answer are off-topic on this site. –  Oct 04 '16 at 02:55

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Quoting the List of unsolved problems in mathematics - Analysis it is yet unknown whether $\pi+e$, $\pi \cdot e$, $\frac{\pi}{e}$ and $\pi^e$ are rational, algebraic irrational, or transcendental.

dxiv
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