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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?

Mathematics
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-Because when you add and multiply rational numbers you will still obatain a fraction or ratio of two integers. -No -Yes Is this the best explanation?
Yes.
If not , please give me some hints :)

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Other answers:

If you need counter-proofs: 1) No counter-proof. 2) \(\rm i\times i = 1\) 3) No counter-proof.

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