Can the product of an irrational and any real number be a rational?

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- Jul 2nd 2010, 12:23 AMtheonProperty of Irrational
Can the product of an irrational and any real number be a rational?

- Jul 2nd 2010, 12:36 AMmelese
- Jul 2nd 2010, 12:36 AMpickslides
What you are asking and what you really want to know might be two different things.

Remember $\displaystyle \mathbb{Q} \subset \mathbb{R}$

I can think of an irrational number that is multiplied by a real that gives a rational. But this does not work for all cases. Is this what you want to know? - Jul 2nd 2010, 01:13 AMtheon
You're right. Based on your post, I'd appreciate greater clarity.

Are the instances where it works seperable, as one or more groups, from cases where it doesn't? If so, how might we described each group? - Jul 2nd 2010, 02:47 AMCaptainBlack
- Jul 2nd 2010, 05:25 AMtheon
OK. Hope the following is better.

Pickslides had said: "I can think of an irrational number that is multiplied by a real that gives a rational. But this does not work for all cases."

So, since the product of an irrational and a real is a rational in some cases but not in other cases, are there rules by which we can know in advance whether the outcome would be an irrational or a rational?

(e.g. irrational x rational = irrational ... or... irrational x irrational = rational,... or... irrational x itself = rational... etc.) - Jul 2nd 2010, 11:54 PMCaptainBlack
- Jul 3rd 2010, 01:05 AMtheon