Question

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

103
Start Fraction 10 over 3 end fraction

3.1
3.1

165
Start Fraction 16 over 5 end fraction

3.4
3.4
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Answer 1

To find a rational number between \(\sqrt{10}\) and \(\sqrt{11}\), let's first approximate these values:

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

Now we can look for rational numbers that fall between these two values.

Among the options provided:

1. \( \frac{10}{3} \approx 3.333 \) (not between \(\sqrt{10}\) and \(\sqrt{11}\))
2. \( 3.1 \) (between \(\sqrt{10}\) and \(\sqrt{11}\))
3. \( \frac{16}{5} = 3.2 \) (between \(\sqrt{10}\) and \(\sqrt{11}\))
4. \( 3.4 \) (not between \(\sqrt{10}\) and \(\sqrt{11}\))

Thus, valid responses that are rational numbers between \(\sqrt{10}\) and \(\sqrt{11}\) are:

- \(3.1\)
- \(\frac{16}{5} (3.2)\)

So the answer could be either \(3.1\) or \(\frac{16}{5}\).