To determine which of the given options is a rational number between \(\sqrt{10}\) and \(\sqrt{11}\), we first need to find the approximate values of \(\sqrt{10}\) and \(\sqrt{11}\).
\[ \sqrt{10} \approx 3.162 \] \[ \sqrt{11} \approx 3.317 \]
Now we are looking for a rational number that lies strictly between these two values (approximately between 3.162 and 3.317).
Let's evaluate each option:
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16 over 5: \[ \frac{16}{5} = 3.2 \] This value is between 3.162 and 3.317.
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3.4: This value is greater than 3.317, so it is not between \(\sqrt{10}\) and \(\sqrt{11}\).
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10 over 3: \[ \frac{10}{3} \approx 3.333 \] This value is greater than 3.317, so it is not between \(\sqrt{10}\) and \(\sqrt{11}\).
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3.1: This value is less than 3.162, so it is not between \(\sqrt{10}\) and \(\sqrt{11}\).
The only option that is between \(\sqrt{10}\) and \(\sqrt{11}\) is:
\(\frac{16}{5}\) (or 3.2).
1 answer