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OpenStudy (anonymous):
Below is a proof showing that the sum of a rational number and an irrational number is an irrational number. Let a be a rational number and b be an irrational number. Assume that a + b = x and that x is rational. Then b = x – a = x + (–a). x + (–a) is rational because_______________________. However, it was stated that b is an irrational number. This is a contradiction. Therefore, the assumption that x is rational in the equation a + b = x must be incorrect, and x should be an irrational number. In conclusion, the sum of a rational number and an irrational number is irrational.
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