Question

hich of these is a rational number that comes between 7–√
and 8–√
?(1 point)
Responses

56
5 sixths

197
19 sevenths

34
3 fourths

63

Answer 1

To determine which of the given options is a rational number that lies between \(\sqrt{7}\) and \(\sqrt{8}\), we first need to evaluate the approximate values of \(\sqrt{7}\) and \(\sqrt{8}\):

- \(\sqrt{7} \approx 2.64575\)
- \(\sqrt{8} \approx 2.82843\)

Now, we can check each of the options:

1. **\(56\)**: This is much larger than \(\sqrt{8}\).
2. **\(\frac{5}{6}\)**: This is approximately \(0.8333\), which is less than \(\sqrt{7}\).
3. **\(\frac{19}{7}\)**: This is approximately \(2.7142857\), which falls between \(\sqrt{7}\) and \(\sqrt{8}\).
4. **\(\frac{3}{4}\)**: This is \(0.75\), which is also less than \(\sqrt{7}\).
5. **\(63\)**: This is much larger than \(\sqrt{8}\).

From the evaluations, the only rational number that lies between \(\sqrt{7}\) and \(\sqrt{8}\) is **\(\frac{19}{7}\)**.