## Thinking Mathematically (6th Edition)

$6\sqrt{3}$miles, 10.4miles
For the height h and d as the distance, it varies as: $d=\sqrt{\frac{3h}{2}}$ (I) The height of the pool deck on the cruise ship above water is 72 feet, the distance can be calculated by inputting the value of height in (I): $d=\sqrt{\frac{3\left( 72 \right)}{2}}$ $d=\sqrt{\frac{3.72}{2}}$ (II) Now, if m and n are representing positive numbers, then, \begin{align} & \sqrt{mn}=\sqrt{m}.\sqrt{n} \\ & \sqrt{m}.\sqrt{n}=\sqrt{mn} \end{align} (III) Use (III) in (II) to get, \begin{align} & d=\sqrt{\frac{3\times 3\times 3\times 2\times 2\times 2}{2}} \\ & =\sqrt{3\times }\left( \sqrt{3}\times \sqrt{3} \right)\times \left( \sqrt{2}\times \sqrt{2} \right) \\ & =6\sqrt{3} \end{align} The distance to which a person can see is $6\sqrt{3}$miles. The value $6\sqrt{3}$is in radical form, the input for calculating the tenth of a mile on the calculator are as follows: Step1: Press 6 and then press $\times$key. Step2: Press the ${{2}^{nd}}$key and press ${{x}^{2}}$key. Step3: Close the bracket and press ENTER key. The distance to which a person can see to the nearest of a mile is 10.4 miles.