Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.4 The Irrational Numbers - Exercise Set 5.4 - Page 296: 75


\[6\sqrt{3}\]miles, 10.4miles

Work Step by Step

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.
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