Part B Now consider the product of a nonzero rational number and an irrational number. Again, assume x = , where a and b are integers and b ≠ 0. This time let y be an irrational number. If we assume the product x · y is rational, we can set the product equal to , where m and n are integers and n ≠ 0. The steps for solving this equation for y are shown.

Based on what we established about the classification of y and using the closure of integers, what does the equation tell you about the type of number y must be for the product to be rational? What conclusion can you now make about the result of multiplying a rational and an irrational number?