Some Irrational Numbers can be multiplied by another irrational number to yield a rational number - for example the square root of 2 is irrational but if you multiply it by itself, you get 2 - which is rational.
Irrational roots of numbers can yield rational numbers if they are raised to the appropriate power
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10.01 is a rational number
Rational
Such a product is always irrational - unless the rational number happens to be zero.
The sum of a rational and irrational number must be an irrational number.
rational * irrational = irrational.