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

Question

Responses

3.1
3.1

165
Start Fraction 16 over 5 end fraction

3.4
3.4

103
Start Fraction 10 over 3 end fraction

Answer 1

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

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

Next, we look for a rational number that lies between these two values.

Now, let’s evaluate the options provided:

1. 3.1: This is approximately 3.1, which is less than 3.162.
2. \(\frac{16}{5}\): This equals 3.2, which falls between \(\sqrt{10}\) and \(\sqrt{11}\).
3. 3.4: This is greater than \(\sqrt{11}\).
4. \(\frac{10}{3}\): This equals approximately 3.333, which is greater than \(\sqrt{11}\).

The only option that fits within the bounds of \(\sqrt{10}\) and \(\sqrt{11}\) is \(\frac{16}{5}\).

Answer: \(\frac{16}{5}\) (or 3.2).