To prove that 2√⋅7 is irrational, assume the product is rational and set it equal to a/b, where b is not equal to 0. Isolating the radical gives 2√ = a/7b. The right side of the equation is (irrational, rational). Because the left side of the equation is (irrational, rational), this is a contradiction. Therefore, the assumption is wrong, and the product is (rational, irrational).

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