Yes, an irrational number divided by an irrational number will usually be an irrational number, but not always. For example, pi / (3pi) is 1/3, which is a rational number, but pi/e is an irrational number.
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No.3*sqrt(2) and sqrt(2) are irrational. But their quotient is 3, which is rational.
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An irrational number is a number that has no definite end. So it can't be multiplied or divided by anything to make a rational number that does have a definite end.
from another wikianswers page: say that 'a' is rational, and that 'b' is irrational. assume that a + b equals a rational number, called c. so a + b = c subtract a from both sides. you get b = c - a. but c - a is a rational number subtracted from a rational number, which should equal another rational number. However, b is an irrational number in our equation, so our assumption that a + b equals a rational number must be wrong.
In math, it means any number that can't be written asone whole number divided by another whole number.