if for a real number $n$ , $n^x$ where $x$ is an irrational number. What is nature of number $n^x$ ? Possible values or how to determine nature of number $n^x$ ?
value of square root of 2 rays to square root of 2.
if for a real number $n$ , $n^x$ where $x$ is an irrational number. What is nature of number $n^x$ ? Possible values or how to determine nature of number $n^x$ ?
value of square root of 2 rays to square root of 2.
There is an engaging theorem that says that there exist two irrational numbers $x,y$ such that $x^y$ is rational.
The engaging part is the proof:
Consider $x=\sqrt 2^\sqrt 2$. If $x$ is rational the theorem is proved. If not, $x^\sqrt 2=2$, and the theorem is proved.