Question

Which of the following is a rational number between 5 and 5 1/4 ?
square root of 26
5 1/8
5 2/5
5 1/3

Answer 1

To determine which of the options is a rational number between 5 and \( 5 \frac{1}{4} \) (or 5.25), let's evaluate each choice:

1. **Square root of 26**:
\( \sqrt{26} \) is approximately 5.099. This is between 5 and 5.25.

2. **\( 5 \frac{1}{8} \)**:
This is equal to \( 5 + 0.125 = 5.125 \), which is also between 5 and 5.25.

3. **\( 5 \frac{2}{5} \)**:
This is equal to \( 5 + 0.4 = 5.4 \), which is greater than 5.25.

4. **\( 5 \frac{1}{3} \)**:
This is equal to \( 5 + \frac{1}{3} \approx 5.333 \), which is also greater than 5.25.

Based on this analysis, the rational numbers that fall between 5 and \( 5 \frac{1}{4} \) are:

- **Square root of 26**
- **\( 5 \frac{1}{8} \)**

So, both \( \sqrt{26} \) and \( 5 \frac{1}{8} \) are rational numbers between 5 and \( 5 \frac{1}{4} \).