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Yes.
Take any rational number p.
Let a = any number that is not a power of 10, so that log(a) is irrational.
and let b = p/log(a).
log(a) is irrational so 1/log(a) must be irrational. That is, both log(a) and log(b) are irrational.
But log(a)*log(b) = log(a)*[p/log(a)] = p which is rational.
In the above case all logs are to base 10, but any other base can be used.
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When you multiply two irrational numbers the result is called what?
If you multiply two irrational numbers, the result can be rational, or irrational.
What is an irrational plus two rational numbers?
Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.
Are rational numbers is an irrational numbers?
yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
Are the sum of two rational numbers rational or irrational?
They are always rational.
Is the product of two rational number irrational or rational?
It is always rational.
