Yes.
[2-sqrt(3)]*[2+sqrt(3)] = 4 - 3 = 1
In general, [x-sqrt(y)]*[x+sqrt(y)] = x-squared + y, is rational.
x-sqrt(y) and x+sqrt(y) are called conjugates of one another. This property is used to remove irrational denominators.
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If you multiply two irrational numbers, the result can be rational, or irrational.
no
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.
All irrational numbers are not rational.
In general, no. It is possible though. (2pi)/pi is rational. pi2/pi is irrational. The ratio of two rationals numbers is always rational and the ratio of a rational and an irrational is always irrational.