Rational ^ sqrt(5) = rational ?

1. Aug 31, 2008

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
$$x^{\sqrt{5}}=y$$
Is it possible?
Probably not, but I cannot prove it :(

2. Aug 31, 2008

gel

Last edited by a moderator: Apr 23, 2017 at 3:21 PM