Show an example of a rational number that is between 10−−√ and 11−−√ .(1 point)

Question

Responses

3.1
3.1

103
Start Fraction 10 over 3 end fraction

165
Start Fraction 16 over 5 end fraction

3.4

Answer 1

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

• \(\sqrt{10} \approx 3.162\)
• \(\sqrt{11} \approx 3.317\)

Now, we want to find a rational number that lies between \(3.162\) and \(3.317\).

Let's evaluate the responses:

1. 3.1: This is less than \(3.162\).
2. \(\frac{10}{3}\): This is approximately \(3.333\), which is greater than \(3.317\).
3. \(\frac{16}{5}\): This is \(3.2\), which falls between \(3.162\) and \(3.317\).
4. 3.4: This is greater than \(3.317\).

Therefore, the correct answer is \(\frac{16}{5}\), as it lies between \(\sqrt{10}\) and \(\sqrt{11}\).