Question

Which of the following is rational?(1 point)
Responses

3–√ ×3–√
Start Root 3 End Root times Start Root 3 End Root

13√
Start Fraction 1 over Start Root 3 End Root End Fraction

3√1
Start Fraction Start Root 3 End Root over 1 End Fraction

3–√+3–√

Answer 1

To determine which of the given expressions is rational, let's analyze each one:

1. \( \sqrt{3} \times \sqrt{3} \) = \( 3 \) (this is rational)

2. \( \frac{1}{\sqrt{3}} \) (this is not rational because it's not a terminating or repeating decimal).

3. \( \frac{\sqrt{3}}{1} \) = \( \sqrt{3} \) (this is not rational).

4. \( \sqrt{3} + \sqrt{3} \) = \( 2\sqrt{3} \) (this is not rational).

From the analysis above, the only rational expression is:

\( \sqrt{3} \times \sqrt{3} = 3 \).