Question

Which of these is a rational number that comes between the square root of 7 and the square root of 8?
- 5/8
-19/7
-3/4
-6/3

Answer 1

To determine which of the given options is a rational number that falls between the square root of 7 and the square root of 8, we first need to calculate the approximate values of these square roots.

1. **Calculate square roots:**
- \( \sqrt{7} \) is approximately 2.645.
- \( \sqrt{8} \) is approximately 2.828.

Now, we want to find a rational number that lies in the interval (2.645, 2.828).

2. **Evaluate the options:**

- **5/8:**
\[
\frac{5}{8} = 0.625 \quad (\text{not between 2.645 and 2.828})
\]

- **19/7:**
\[
\frac{19}{7} \approx 2.714 \quad (\text{this is between 2.645 and 2.828})
\]

- **3/4:**
\[
\frac{3}{4} = 0.75 \quad (\text{not between 2.645 and 2.828})
\]

- **6/3:**
\[
\frac{6}{3} = 2 \quad (\text{not between 2.645 and 2.828})
\]

3. **Conclusion:**
The only rational number among the provided options that lies between the square root of 7 and the square root of 8 is \( \frac{19}{7} \).