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?

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) (Show Source): You can put this solution on YOUR website!
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 .

Dividing both sides of the equation by A results in:

.

p was chosen as an integer, and since A is a whole number and q is an integer, Aq must be an integer. Therefore 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.

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