Now consider the product of a nonzero rational number and an irrational number. Again, assume x = 9, 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.
Statement
Reason
y=
y=
..y=
substitution
b
G
a
multiplication property of equality
Simplify.
y=
m. b
no
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?