Question

show an example of a rational number that is between radical 10 and radical 11

A. 3.1
B. 10/3
C. 3.4
D. 16/5

Answer 1

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

1. \(\sqrt{10} \approx 3.162\)
2. \(\sqrt{11} \approx 3.317\)

Now we are looking for a rational number between these two values. Let’s evaluate the options given:

A. \(3.1\) - This is less than \(3.162\), so it is not between \(\sqrt{10}\) and \(\sqrt{11}\).

B. \(\frac{10}{3} \approx 3.333\) - This is greater than \(\sqrt{11}\), so it is not between.

C. \(3.4\) - This is also greater than \(\sqrt{11}\), so it cannot be between.

D. \(\frac{16}{5} = 3.2\) - This is indeed between \(3.162\) and \(3.317\).

Thus, the correct answer is \(D. \frac{16}{5}\).