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

1 answer

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
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