Question

Choose whether each statement is "Always," "Sometimes," or "Never" true.

Response area with 12 radio buttons within 4 groups.
Statement True?
The sum of a rational number and an irrational number is irrational.

Always

Sometimes

Never

The sum of an irrational number and an irrational number is irrational.

Always

Sometimes

Never

The product of a rational number and a rational number is rational. Always Sometimes Never
The product of an irrational number and an irrational number is irrational. Always Sometimes Never

Answer 1

Here are the answers for each statement:

1. **The sum of a rational number and an irrational number is irrational.**
- **Always**

2. **The sum of an irrational number and an irrational number is irrational.**
- **Sometimes** (For example, \(\sqrt{2} + (-\sqrt{2}) = 0\), which is rational.)

3. **The product of a rational number and a rational number is rational.**
- **Always**

4. **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:

1. Always
2. Sometimes
3. Always
4. Sometimes