To determine between which pair of rational numbers \(\sqrt{18}\) lies, we first need to approximate \(\sqrt{18}\).
We know that:
\[ \sqrt{16} = 4 \] \[ \sqrt{25} = 5 \]
Since \(16 < 18 < 25\), it follows that:
\[ 4 < \sqrt{18} < 5 \]
Next, we can refine this approximation. Since \(18\) is closer to \(16\) and \(25\), we can check \(4.2\) and \(4.3\):
Calculating \(4.2^2\):
\[ 4.2^2 = 17.64 \]
Calculating \(4.3^2\):
\[ 4.3^2 = 18.49 \]
Now we see that:
\[ 4.2^2 < 18 < 4.3^2 \]
This means that \(\sqrt{18}\) is between \(4.2\) and \(4.3\).
Thus, the answer is:
A. Between 4.2 and 4.3.
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