Establish the existence of two irrational numbers A and B, such that the number A^B is rational, or prove that such numbers do not exist.

Let X = sqr(2)^sqr(2), and B = sqr(2).
Either X is irrational; then, A = X, and A^B = [ sqr(2)^sqr(2) ] ^sqr(2) = 2 is rational.
Or X is rational; then A = B, and A^B = X.

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