HardMath and Logic
Irrational number ^ irrational power = rational?
Riddle
Irrational number ^ irrational power = rational?
Choose an answer
A.No
B.Only if one is zero
C.Only for pi
D.Yes
Hint: It's a word with 3 letters, starting with "Y".
Answer
Yes
Why this is the answer
Consider x = sqrt(2)^sqrt(2). If x is rational, we are done. If x is irrational, then x^sqrt(2) = (sqrt(2)^sqrt(2))^sqrt(2) = sqrt(2)^2 = 2, which is rational.
This riddle is filed under Expert Riddles for Adults and rated Hard.
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