Draft:Bpow32

The following problem was suggested by John Haverhals. Many thanks.

You may recall that a real number is called rational if it can be written as a fraction with integers in both the numerator and denominator, otherwise it's called irrational . There are many irrational real numbers; for example, if n is any positive integer which is not a perfect square, then <m>\sqrt{n}</m> is irrational. Find two irrational numbers, a and b, so that <m>a^b</m> is an integer.

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.