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An irrational number is a number whose decimal expansion goes on forever, never terminating or repeating. It would seem that using irrationals to do arithmetic would therefore lead to some pretty complicated expressions. However, this isn't always so. Consider the square root of 8 and the square root of 18. Although both numbers are irrational, their product is 12, a rational number.
Let's define a and b to be two irrational numbers.
Is it possible for the sum or difference of a and b to be a rational number?
Further, is it possible for ab (a to the b power) to be rational?
Both parts must be answered with an explanation for you to receive credit for a correct solution.
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