Question

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

3√1
the fraction with numerator square root of 3 and denominator 1

3–√ +3–√
3–√ +3–√

3 −−√ × 3–√
3 −−√ × 3–√

13√

Answer 1

pick one

Answer 2

To determine which expressions are rational, let's analyze each option:

1. **3√1**: This simplifies to \(3 \cdot 1 = 3\), which is a rational number.

2. **the fraction with numerator square root of 3 and denominator 1**: This is \(\frac{\sqrt{3}}{1}\), which is simply \(\sqrt{3}\). Since \(\sqrt{3}\) is an irrational number, this expression is not rational.

3. **3–√ + 3–√**: This is \( \sqrt{3} + \sqrt{3} = 2\sqrt{3} \). Since \(\sqrt{3}\) is irrational, \(2\sqrt{3}\) is also irrational. Therefore, this expression is not rational.

4. **3 −−√ × 3–√**: This simplifies to \(\sqrt{3} \cdot \sqrt{3} = 3\). Since 3 is a rational number, this expression is rational.

5. **13√**: This refers to \(\sqrt{13}\), which is also irrational.

From the analysis, the rational expressions are:

- **3√1** (which equals 3)
- **3 −−√ × 3–√** (which equals 3)

Thus, both options 1 and the operation represented in option 4 are rational.

Answer 3

The rational expression among the options is:

**3√1** (which equals 3).