Show an example of a rational number that is between the square root of10 and the square root of11. (1 point)

1 answer

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

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

Now, we can choose a rational number that falls between these two values. A simple choice would be \(3.25\) because:

\[ 3.162 < 3.25 < 3.317 \]

Thus, \(3.25\) is a rational number that lies between \(\sqrt{10}\) and \(\sqrt{11}\).

Alternatively, you could also choose \(\frac{13}{4} = 3.25\), which is another way to represent that rational number.