Hard
Math and Logic
Irrational number ^ irrational power = rational?
Choose an answer
A.No
B.Only if one is zero
C.Only for pi
D.Yes
Answer: Yes
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.