# Chapter 5 - Number Theory and the Real Number System - 5.4 The Irrational Numbers - Exercise Set 5.4 - Page 296: 76

$6\sqrt{5}\text{ miles}=13.4\text{ miles}$

#### Work Step by Step

Substitute $120$ for $h$ in the provided formula and calculate $d$. That is., \begin{align} & d=\sqrt{\frac{3h}{2}} \\ & =\sqrt{\frac{3\times 120}{2}} \\ & =\sqrt{180} \end{align} Write $180$ into its prime factors and take square root. That is., \begin{align} & d=\sqrt{180} \\ & =\sqrt{{{2}^{2}}\cdot {{3}^{2}}\cdot 5} \\ & =\left( 2\cdot 3 \right)\sqrt{5} \\ & =6\sqrt{5} \end{align} Now, use calculator to find the values in decimal. So, \begin{align} & 6\sqrt{5}=13.41 \\ & \simeq 13.4 \end{align} Thus, the distance that can be seen is $6\sqrt{5}\text{ miles}=13.4\text{ miles}$

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