Chapter 4.7, Problem 57HP

To determine

To find the number that does not belong with the other three.

Answer to Problem 57HP

  $\sqrt{50}\text{ is an irrational number}\text{.}$

Explanation of Solution

Given information:

  $\left(\text{a}\right)50.\overline{1}\left(\text{b}\right)-\frac{50}{2}\left(\text{c}\right)-50.1\left(\text{d}\right)\sqrt{50}$

Calculation : The number that does not belong with the other three is obtained as,

  $\begin{array}{l}\left(\text{a}\right)50.\overline{1}\text{ since }50.\overline{1}=\mathrm{50.111111.....}\text{this number is a rational number}\text{.}\\ \left(\text{b}\right)-\frac{50}{2}\text{ since}-\frac{50}{2}=-25\text{ this number is a rational number}\text{.}\\ \left(\text{c}\right)-50.1\text{ since}-50.1\text{ this number is a rational number}\text{.}\\ \left(\text{d}\right)\sqrt{50}\text{ since}\sqrt{50}=\mathrm{7.071067812.......}\text{ this number is a irrational number}\text{.}\\ \text{Hence }\sqrt{50}\text{ is an irrational number}\text{. so, }\sqrt{50}\text{ does not belong to other three }\end{array}$