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

Question

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