Chapter 7.1, Problem 4MRE

To determine

To Simplify:

  $\sqrt{98}-\sqrt{8}$

Answer to Problem 4MRE

  $\text{5}\sqrt{2}$

Explanation of Solution

Given:

The expression is :

  $\sqrt{98}-\sqrt{8}$

Calculation:

Given:

  $\begin{array}{l}\sqrt{98}-\sqrt{8}\\ =\sqrt{2\cdot 49}-\sqrt{2\cdot 4}\\ =\sqrt{2\cdot 7^2}-\sqrt{2\cdot 2^2}\mathrm{...............}[\text{factor into squares]}\\ \text{=7}\sqrt{2}-2\sqrt{2}\\ =(7-2)\sqrt{2}\mathrm{........................}[\text{combine like terms]}\\ \text{=5}\sqrt{2}\end{array}$

So,

  $\text{5}\sqrt{2}$ is the solution.