Chapter 12.4, Problem 64SR

To determine

To find: Simplify.

Answer to Problem 64SR

  $\sqrt{{\left(x-4\right)}^2}=x-4$

Explanation of Solution

Given information:

  $\sqrt{{\left(x-4\right)}^2}$

  $\sqrt{{\left(x-4\right)}^2}$

  $\begin{array}{l}\sqrt{{\left(x-4\right)}^2}={\left({\left(x-4\right)}^2\right)}^{\frac{1}{2}}\\ \Rightarrow \sqrt{{\left(x-4\right)}^2}={\left(x-4\right)}^{2\times \frac{1}{2}}\\ \Rightarrow \sqrt{{\left(x-4\right)}^2}={\left(x-4\right)}^1\\ \Rightarrow \sqrt{{\left(x-4\right)}^2}=x-4\end{array}$

Therefore,

  $\sqrt{{\left(x-4\right)}^2}=x-4$