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The number \sqrt{2}^\sqrt{2}, is it rational, an algebraic irrational or is it transcendental?

Recall that a rational number can be expressed as p/qp/q for integers p,qp, q with q0q \neq 0. An algebraic irrational number α\alpha is a solution to the equation P(x)=0P(x) = 0, where P(x)P(x) is a polynomial with rational coefficients. A transcendental number is a real number that is irrational but not an algebraic irrational.

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