SOLUTION: Prove or disprove the product of a rational and an irrational is irrational

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Question 488495: Prove or disprove the product of a rational and an irrational is irrational
Answer by richard1234(7193) About Me  (Show Source):
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Product of a rational and irrational is always irrational. Assume that on the contrary that a is rational, b is irrational, and their product c is rational. Then





The LHS is irrational, while the RHS is a ratio of two rationals (also rational), hence contradiction.