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 mand n are integers and n + 0. The steps for
solving this equation for y are shown.
Reason
Statement
x. y =
y="
substitution
y =
multiplication property of equality
w
mb
y =
na
Simplify
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?