Higher Roots: example 9.90

We use the absolute value to be sure to get the positive root.

1. ⓐ$\begin{array}{ccc}& & \sqrt{x^2}\hfill \\ \text{Since}{\left(x\right)}^2=x^2\text{and we want the positive root.}\hfill & & \left|x\right|\hfill \end{array}$
2. ⓑ
   $\begin{array}{ccc}& & \sqrt[3]{n^3}\hfill \\ \begin{array}{c}\text{Since}{\left(n\right)}^3=n^3.\text{It is an odd root so there is}\hfill \\ \text{no need for an absolute value sign.}\hfill \end{array}\hfill & & n\hfill \end{array}$
3. ⓒ
   $\begin{array}{ccc}& & \sqrt[4]{p^4}\hfill \\ \text{Since}{\left(p\right)}^4=p^4\text{and we want the positive root.}\hfill & & \left|p\right|\hfill \end{array}$
4. ⓓ
   $\begin{array}{ccc}& & \sqrt[5]{y^5}\hfill \\ \begin{array}{c}\text{Since}{\left(y\right)}^5=y^5.\text{It is an odd root so there}\hfill \\ \text{is no need for an absolute value sign.}\hfill \end{array}\hfill & & y\hfill \end{array}$