Part D Now examine the sum of a rational number, y, and an irrational number, x. The rational number y can be written as y =
where a and b are integers and b +0. Leave the irrational number x as x because it can't be written as the ratio of two
integers.
Let's look at a proof by contradiction. In other words, we're trying to show that x + y is equal to a rational number instead
of an irrational number. Let the sum equal where mand n are integers and n0. The process for rewriting the sum for
x is shown
Statement
Reason
o
substitution
x +
subtraction property of equality
n
() () - (A) ()
Create common denominators
X
bn
bran
bi
Simplify
х
Based on what we established about the classification of x and using the closure of integers, what does the equation tell
you about the type of number x must be for the sum to be rational? What conclusion can I now make about the result
of adding a rational and an irrational number?
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