Part B Now consider the product of a nonzero rational number and an irrational number. Again, assume x = 8
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.
or
Statement
Reason
ts
x. y =
y =
n
substitution
y =
multiplication property of equality
b
y =
mb
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?
B
7
y X
X Х.
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