2011/029) can x^y be rational for both irrational x and y

we know that sum and product of irrational x and y can be rational

(a + sqrt(b)) + (a- sqrt(b))= 2a

and product = a^2 - b^2

so taking a and b rational such that sqrt(b) is irrational we can get easily


but for power

say x = sqrt(2) and y = sqrt(2)


is x^y rational

we do noy know

but if it is then we are through

and if it is not then (x^y)^y = 2 whhich is rational

hence x^y can be rational for both irrational x and y