Question

Which of the following is rational?(1 point) Responses 13√ Start Fraction 1 over Start Root 3 End Root End Fraction 3–√ ×3–√ Start Root 3 End Root times Start Root 3 End Root 3–√+3–√ Start Root 3 End Root plus Start Root 3 End Root 3√1

Answer 1

To determine whether each of the following expressions is rational, we review them one by one.

1. **\( 13\sqrt{1} \)**: This simplifies to \( 13 \), which is a rational number.

2. **\( \frac{1}{\sqrt{3}} \)**: This expression is not rational because it involves the square root of 3, which is an irrational number.

3. **\( 3\sqrt{3} \times \sqrt{3} \)**: Simplifying this gives us \( 3 \times 3 = 9 \), which is rational.

4. **\( 3\sqrt{3} + \sqrt{3} \)**: This simplifies to \( (3 + 1)\sqrt{3} = 4\sqrt{3} \), which is not rational because it includes the irrational number \( \sqrt{3} \).

5. **\( \sqrt[3]{1} \)**: This simplifies to \( 1 \), which is rational.

In summary, the rational expressions among the options given are:
- \( 13\sqrt{1} \) (which equals 13)
- \( 3\sqrt{3} \times \sqrt{3} \) (which equals 9)
- \( \sqrt[3]{1} \) (which equals 1)

Therefore, the rational options are \( 13\sqrt{1} \), \( 3\sqrt{3} \times \sqrt{3} \), and \( \sqrt[3]{1} \).