Question
Which of the following is rational?(1 point)
Responses
3–√+3–√
Start Root 3 End Root plus Start Root 3 End Root
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
13√
Responses
3–√+3–√
Start Root 3 End Root plus Start Root 3 End Root
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
13√
Answers
Answered by
GPT-4o mini
To determine which of the given expressions is rational, let's analyze each option:
1. **\( \sqrt{3} + \sqrt{3} \)**:
This simplifies to \( 2\sqrt{3} \), which is not rational (as it involves the irrational number \( \sqrt{3} \)).
2. **\( \frac{\sqrt{3}}{1} \)**:
This is simply \( \sqrt{3} \), which is not rational.
3. **\( \sqrt{3} \times \sqrt{3} \)**:
This simplifies to \( 3 \), which is rational.
4. **\( 13\sqrt{} \)** (assuming a typographical error, likely meant to be \( 13\sqrt{3} \) or something similar):
Regardless, any expression of the form \( k\sqrt{3} \) where \( k \) is a non-zero rational number is still irrational, so this would not be rational.
Therefore, the only rational expression among the options is:
**\( \sqrt{3} \times \sqrt{3} = 3 \)**.
1. **\( \sqrt{3} + \sqrt{3} \)**:
This simplifies to \( 2\sqrt{3} \), which is not rational (as it involves the irrational number \( \sqrt{3} \)).
2. **\( \frac{\sqrt{3}}{1} \)**:
This is simply \( \sqrt{3} \), which is not rational.
3. **\( \sqrt{3} \times \sqrt{3} \)**:
This simplifies to \( 3 \), which is rational.
4. **\( 13\sqrt{} \)** (assuming a typographical error, likely meant to be \( 13\sqrt{3} \) or something similar):
Regardless, any expression of the form \( k\sqrt{3} \) where \( k \) is a non-zero rational number is still irrational, so this would not be rational.
Therefore, the only rational expression among the options is:
**\( \sqrt{3} \times \sqrt{3} = 3 \)**.