Here are the answers for each statement:
-
The sum of a rational number and an irrational number is irrational.
- Always
-
The sum of an irrational number and an irrational number is irrational.
- Sometimes (For example, \(\sqrt{2} + (-\sqrt{2}) = 0\), which is rational.)
-
The product of a rational number and a rational number is rational.
- Always
-
The product of an irrational number and an irrational number is irrational.
- Sometimes (For example, \(\sqrt{2} \times \sqrt{2} = 2\), which is rational.)
So the final answers are:
- Always
- Sometimes
- Always
- Sometimes