Question
Which of the following is rational?(1 point) Responses 3√1 Start Fraction Start Root 3 End Root over 1 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 13√
Answers
GPT-4o mini
To determine which of the expressions are rational, we need to look at each option.
1. **\( \sqrt[3]{1} \)**: This is equal to 1, which is a rational number.
2. **\(\frac{\sqrt{3}}{1}\)**: This is simply \(\sqrt{3}\), which is an irrational number.
3. **\( \sqrt{3} \times \sqrt{3} \)**: This equals 3, which is a rational number.
4. **\( \sqrt{3} + \sqrt{3} \)**: This equals \(2\sqrt{3}\), which is still irrational due to the involvement of \(\sqrt{3}\).
5. **\( 13\sqrt{3} \)**: This is an irrational number because it still contains \(\sqrt{3}\).
From the descriptions above, the rational numbers from the given expressions are:
- **\( \sqrt[3]{1} = 1 \)**
- **\( \sqrt{3} \times \sqrt{3} = 3 \)**
Thus, both \( \sqrt[3]{1} \) and \(\sqrt{3} \times \sqrt{3}\) are rational numbers.
1. **\( \sqrt[3]{1} \)**: This is equal to 1, which is a rational number.
2. **\(\frac{\sqrt{3}}{1}\)**: This is simply \(\sqrt{3}\), which is an irrational number.
3. **\( \sqrt{3} \times \sqrt{3} \)**: This equals 3, which is a rational number.
4. **\( \sqrt{3} + \sqrt{3} \)**: This equals \(2\sqrt{3}\), which is still irrational due to the involvement of \(\sqrt{3}\).
5. **\( 13\sqrt{3} \)**: This is an irrational number because it still contains \(\sqrt{3}\).
From the descriptions above, the rational numbers from the given expressions are:
- **\( \sqrt[3]{1} = 1 \)**
- **\( \sqrt{3} \times \sqrt{3} = 3 \)**
Thus, both \( \sqrt[3]{1} \) and \(\sqrt{3} \times \sqrt{3}\) are rational numbers.