SOLUTION: Explain why the sum, the difference, and the product of two rational numbers are rational numbers. Is the product of two irrational numbers necessarily irrational? What about the s

Question 483073: Explain why the sum, the difference, and the product of two rational numbers are rational numbers. Is the product of two irrational numbers necessarily irrational? What about the sum?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Sum, difference, and product of two rational numbers is always rational, it can be shown similar to a way we add, subtract, and multiply fractions. If a/b, c/d are the two rational numbers then their sum is (ad + bc)/bd, their difference is (ad - bc)/bd, and their product is ac/bd, all of them rational because the numerator and denominator are always integers.

The product and sum of two irrational numbers is not always irrational. For example,

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