rational ^ sqrt(5) = rational ?

Gerenuk

I've programmed an algorithm to numerically compute the logarithm of numbers in phinary base easily. I could avoid float multiplications if I can find a pair of rational numbers x and y such that
[tex]x^{\sqrt{5}}=y[/tex]
Is it possible?
Probably not, but I cannot prove it :(

gel

No, it isn't possible except for the obvious x=y=1. There's a theorem which says that it's impossible.