The square root of 2, for example, is irrational.
sqrt(2)*sqrt(2) = 2 which is rational.
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Yes, multiplying a rational and an irrational number gives an irrational product. For example 3 * pi = 3pi = 9.424789... or 2 * sqrt 2 = 2^(3/2).
If you multiply or divide an irrational number - such as pi - by ANY rational number (except zero), you will ALWAYS get an irrational number.
Sometimes. eg the irrational number √2 squared is 2 which is rational (2 = 2/1) eg the irrational number √(√2) squared is √2 which is irrational.
No. sqrt(2)/pi is not rational.
2 is a rational number and it is also a prime number