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

Question

Responses

5/6
5 over
6

19/7
19 over
7

3/4
3 over

6/3
6 over
3

Answer 1

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

Calculating the square roots:

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

Now, let's evaluate the given options:

1. \( \frac{5}{6} \approx 0.8333 \) (This is less than \( \sqrt{7} \))
2. \( \frac{19}{7} \approx 2.71429 \) (This is between \( \sqrt{7} \) and \( \sqrt{8} \))
3. \( \frac{3}{4} = 0.75 \) (This is less than \( \sqrt{7} \))
4. \( \frac{6}{3} = 2 \) (This is less than \( \sqrt{7} \))

The only rational number from the options that lies between \( \sqrt{7} \) and \( \sqrt{8} \) is:

\( \frac{19}{7} \).