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Question 1207368: Can an irrational number raised to an irrational power yield an answer that is rational? This problem shows that the answer is “yes.” (However, if you study the following solution very carefully, you’ll see that even though we’ve answered the question in the affirmative, we’ve not pinpointed the specific case in which an irrational number raised to an irrational power is rational.)
(a) Let A = (sqrt{2})^(sqrt{2}). Now, either A is rational or A is irrational. If A is rational, we are done. Why?
(b) If A is irrational, we are done. Why?
Hint:Consider A^(sqrt{2}).
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
a soup of words with zero mathematical meaning.
Did I say " . . . with zero mathematical meaning" ?
No. it is not right. It is better to say " with negative mathematical meaning ".
So, it is better to glue up your eyes and ears with adhesive tape
so as not to see or hear this MEGA-gibberish.
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