Find a rational number with one decimal place that is between 17−−√ and 18−−√.

Answer 1

To find a rational number between $\sqrt{17}$ and $\sqrt{18},$ we average these two numbers to get $\frac{\sqrt{17}+\sqrt{18}}{2}.$ In decimal notation, $\sqrt{17}\approx 4.123$ and $\sqrt{18}\approx 4.242.$ Therefore, $\frac{\sqrt{17}+\sqrt{18}}{2}\approx \frac{4.123+4.242}{2}=\frac{8.365}{2}=\boxed{4.183}.$