Question

Show an example of a rational number that is between and
. (1 point)
10
−− √
11
−− √
3.1
3.4
10
3
16
5

Answer 1

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

1. **Calculate the approximate values**:
- \(\sqrt{10} \approx 3.162\)
- \(\sqrt{11} \approx 3.317\)

Now we have the range:
- Lower bound: \(\sqrt{10} \approx 3.162\)
- Upper bound: \(\sqrt{11} \approx 3.317\)

2. **Identify rational numbers within this range**:
A rational number is any number that can be expressed as the quotient of two integers (e.g., \( \frac{a}{b} \)). We can try simple fractions or decimals.

- A rational number that fits in this range would be \(3.2\).

This number is between \(\sqrt{10}\) and \(\sqrt{11}\) because:
\[
3.162 < 3.2 < 3.317
\]

Therefore, **\(3.2\)** is an example of a rational number that lies between \(\sqrt{10}\) and \(\sqrt{11}\).