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to prove that 2√2 is irrational, assume the product is rational and set it equal to a/b, where b is not equal to 0: 2√2 = a/b . isolating the radical gives √2 = a/2b. the left side of the equation is (irrational, rational) . because the right side of the equation is (irrational, rational), this is a contradiction. therefore, the assumption is wrong, and the number 2√2 is (irrational, rational).