SOLUTION: Critical thinking Suppose A is a whole number and B is an irrational number. Is it possible for the product of AB to be a rational number? Explain why or why not?

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Question 124041: Critical thinking
Suppose A is a whole number and B is an irrational number. Is it possible for the product of AB to be a rational number? Explain why or why not?

Answer by solver91311(24713) About Me  (Show Source):
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We are given A is a whole number and B is irrational. Let's assume that the product A*B is rational. That means that there are two integers p and q such that AB=p%2Fq.

Dividing both sides of the equation by A results in:

B=p%2F%28Aq%29.

p was chosen as an integer, and since A is a whole number and q is an integer, Aq must be an integer. Therefore p%2F%28Aq%29 is a rational number.

But that means B must be rational, contradicting the given condition that B be irrational. Therefore the assumption that A*B is rational must be false and A*B must be irrational.