SOLUTION: Prove or disprove the product of a rational and an irrational is irrational
Algebra.Com
Question 488495: Prove or disprove the product of a rational and an irrational is irrational
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
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.
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