Show an example of a rational number that is between √10 and √11.

Question

options:

16 over 5

3.4

10 over 3

3.1

Answer 1

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:

1. 16 over 5: $$\frac{16}{5}=3.2$$ This value is between 3.162 and 3.317.

2. 3.4: This value is greater than 3.317, so it is not between $\sqrt{10}$ and $\sqrt{11}$.

3. 10 over 3: $$\frac{10}{3}\approx 3.333$$ This value is greater than 3.317, so it is not between $\sqrt{10}$ and $\sqrt{11}$.

4. 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).