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Earn +20 ptsQ: Is 0.692 irrational r rational
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Is an irrational number divided by a rational number always irrational?
Yes. The proof is easy. Let x be the irrational number and assume there exists some rational number r = a/b where a and b are integers (that's what it means to be rational). Now suppose x/r is a rational number. Then x/r = (b/a)x = c/d where c and d are some other integers. Since (b/a)x=c/d, then x = bd/ac which means that x itself is rational, but we assumed it was irrational. The contradiction proves that the assertion is wrong. An irrational divided by a rational must be irrational.
Is a rational plus an irrational equals a rational?
No. A rational plus an irrational is always an irrational.
Is -131 rational or irrational?
rational
Is the sum of a rational and irrational number rational or irrational?
It is always irrational.
What is the product of rational and irrational number?
The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.
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