rationalize the denominatorIs there any theorem saying that in below fraction we can't rationalize the...

Lydia Carey

Lydia Carey



rationalize the denominator
Is there any theorem saying that in below fraction we can't rationalize the denominator
2 π
I couldn't find any way and I don't think there is but I was wondering if this actually proved? for example for 1 2 we say
1 2 = 1 × 2 2 × 2 = 2 2
result have meaning if we look at fraction like Division

Answer & Explanation




2022-06-29Added 22 answers

Are you speaking of rationalizing the denominator and the numerator at the same time? If not, a trivial solution would be 2 / π 1 , but that doesn't seem very interesting. So perhaps you are speaking about some sort of manipulation that creates 2 π = p q , where both p and q are rational. But, I would find that greatly disturbing, because then it would be the case that p q is also rational... in which case 2 π would be rational as well.
EDIT: Your example with 2 is similar to the trivial solution above, but, in the case of a radical, might have some more use.
So, yes, you can rationalize the denominator, if you find such action useful. But, would you, in the case of 2 π ?

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