Question

Which of the following is rational?(1 point) Responses 13√ the fraction with numerator 1 and denominator square root of 3 3 −−√ × 3–√ 3 −−√ × 3–√ 3√1 the fraction with numerator square root of 3 and denominator 1 3–√ +3–√

Answer 1

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

1. **13√**: This is \( 13\sqrt{3} \). Since it is a product of a rational number (13) and an irrational number (\(\sqrt{3}\)), it is irrational.

2. **The fraction with numerator 1 and denominator square root of 3**: This is expressed as \( \frac{1}{\sqrt{3}} \). Since the denominator is an irrational number, this fraction is also irrational.

3. **3 −−√ × 3–√**: This can be interpreted as \( \sqrt{3} \times \sqrt{3} = 3\). The product of \(\sqrt{3}\) with itself yields a rational number (3).

4. **3√1**: This can be interpreted as \(\sqrt{3} \cdot 1\), which is \( \sqrt{3} \). This is an irrational number.

5. **The fraction with numerator square root of 3 and denominator 1**: This fraction is \( \frac{\sqrt{3}}{1} = \sqrt{3} \), which is irrational.

6. **3–√ + 3–√**: This represents \( \sqrt{3} + \sqrt{3} = 2\sqrt{3} \). Since it is a rational number (2) multiplied by an irrational number (\(\sqrt{3}\)), it is also irrational.

The only rational number in the options is:

**3 −−√ × 3–√ = 3**.