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 n #0. The process for rewriting the sum for
x is shown
Statement
Reason
substitution
subtraction property of equality
(*) (*) - (4 ()
Create common denominators
x = sme
Simplify
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 you now make about the result
of adding a rational and an irrational number?