Question

Which of the following rational numbers is not between 3–√ and 6–√ ? show you r work

Answer 1

To determine which rational number is not between \(\sqrt{3}\) and \(\sqrt{6}\), we first need to calculate the approximate values of these square roots.

1. **Calculate \(\sqrt{3}\)**:
\[
\sqrt{3} \approx 1.732
\]

2. **Calculate \(\sqrt{6}\)**:
\[
\sqrt{6} \approx 2.449
\]

Now we know that \(\sqrt{3} \approx 1.732\) and \(\sqrt{6} \approx 2.449\). Therefore, we need to identify rational numbers that lie between these two values.

Any rational number \(x\) that satisfies:
\[
\sqrt{3} < x < \sqrt{6}
\]
or
\[
1.732 < x < 2.449
\]
is considered to be between \(\sqrt{3}\) and \(\sqrt{6}\).

Let's check some potential rational numbers:

- **Number 1**: \(1.8\)
- Since \(1.732 < 1.8 < 2.449\), it is between \(\sqrt{3}\) and \(\sqrt{6}\).

- **Number 2**: \(2.3\)
- Since \(1.732 < 2.3 < 2.449\), it is also between \(\sqrt{3}\) and \(\sqrt{6}\).

- **Number 3**: \(2.5\)
- Since \(2.5 > 2.449\), it is not between \(\sqrt{3}\) and \(\sqrt{6}\).

- **Number 4**: \(2\)
- Since \(1.732 < 2 < 2.449\), it is between \(\sqrt{3}\) and \(\sqrt{6}\).

To sum up, among the rational numbers we looked at, **\(2.5\)** is the one that is not between \( \sqrt{3} \) and \( \sqrt{6} \).