To find a rational number with one decimal place that lies between \(\sqrt{17}\) and \(\sqrt{18}\), we start by calculating the approximate values of \(\sqrt{17}\) and \(\sqrt{18}\).
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Estimating \(\sqrt{17}\): \[ \sqrt{16} = 4 \quad \text{and} \quad \sqrt{25} = 5 \] So, \(\sqrt{17}\) is slightly more than 4. A more precise calculation gives: \[ \sqrt{17} \approx 4.123 \]
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Estimating \(\sqrt{18}\): \[ \sqrt{16} = 4 \quad \text{and} \quad \sqrt{25} = 5 \] So, \(\sqrt{18}\) is slightly more than 4. A more precise calculation gives: \[ \sqrt{18} \approx 4.243 \]
Now, we have: \[ \sqrt{17} \approx 4.123 < x < \sqrt{18} \approx 4.243 \]
Next, we look for a rational number with one decimal place within this range.
A suitable choice is \(4.2\), which is greater than \(4.123\) and less than \(4.243\):
\[ \sqrt{17} < 4.2 < \sqrt{18} \]
Thus, the rational number with one decimal place that is between \(\sqrt{17}\) and \(\sqrt{18}\) is: \[ \boxed{4.2} \]
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