Question

Show an example of a rational number that is between 10−−√ and 11−−√.(1 point) Responses 3.1 3.1 165 Start Fraction 16 over 5 end fraction 103 Start Fraction 10 over 3 end fraction 3.4

Answer 1

To find a rational number between \( \sqrt{10} \) and \( \sqrt{11} \), we first determine the approximate values of these square roots:

- \( \sqrt{10} \) is approximately \( 3.162 \).
- \( \sqrt{11} \) is approximately \( 3.317 \).

Now, we need to pick a rational number that lies within this range. Looking at the options provided:

- 3.1 (which is less than \( \sqrt{10} \))
- \( \frac{16}{5} = 3.2 \)
- \( 10/3 \approx 3.333 \) (which is more than \( \sqrt{11} \))
- 3.4 (which is more than \( \sqrt{11} \))

From this, the rational number \( \frac{16}{5} \) (which is equal to 3.2) is between \( \sqrt{10} \) and \( \sqrt{11} \).

So, a rational number that is between \( \sqrt{10} \) and \( \sqrt{11} \) is \( \frac{16}{5} \).