Rational and Irrational Numbers
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Always
The product of a nonzero rational number and an irrational number is irrational.
Always
The product of a rational number and a rational number is rational.
Sometimes
The product of an irrational number and an irrational number is irrational.
Always
The sum of a rational number and a rational number is rational.
Always
The sum of a rational number and an irrational number is irrational.
Sometimes
The sum of an irrational number and an irrational number is irrational.