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.
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Calculate \(\sqrt{3}\): \[ \sqrt{3} \approx 1.732 \]
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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:
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Number 1: \(1.8\)
- Since \(1.732 < 1.8 < 2.449\), it is between \(\sqrt{3}\) and \(\sqrt{6}\).
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Number 2: \(2.3\)
- Since \(1.732 < 2.3 < 2.449\), it is also between \(\sqrt{3}\) and \(\sqrt{6}\).
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Number 3: \(2.5\)
- Since \(2.5 > 2.449\), it is not between \(\sqrt{3}\) and \(\sqrt{6}\).
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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 \( \sqrt{6} \).