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Ryiaz claims it is impossible to prove that a rational number multiplied by an irrational number gives an irrational product. How can you prove this?

A. He's correct; it is impossible to prove in any way.
B. By using a proof by contradiction to show multiplication is a closed operation for rational numbers.
C. By creating a proof that shows directly how multiplying a rational and irrational number leads to an irrational answer.
D. By choosing random numbers to plug into multiplication problems until he's convinced.



Answer :

GinnyAnswer

Final answer:

To show that the product of a rational number and an irrational number results in an irrational number, we utilize proof by contradiction.


Explanation:

Proof by contradiction: To prove that the product of a rational number and an irrational number is irrational, assume the opposite, that the product is rational. Let's say x is rational and y is irrational. If xy were rational, then y would be rational too, which contradicts the assumption that y is irrational. Hence, the product xy must be irrational.


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