Q. 27 - Intermediate Algebra

Question

In the following exercises, simplify using absolute values as necessary. 

$ⓐ \sqrt[5]{u^5} ⓑ \sqrt[8]{v^8}$

Step-by-Step Solution

Answer

Part(a)$\sqrt[5]{u^5}=u$

Part(b)$\sqrt[8]{v^8}=\left|v\right|$

Part(a) Step 1. Given information

$ⓐ \sqrt[5]{u^5}$

 Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{This is an odd indexed root so there is no need for an absolute value sign.}\\ \text{Since the index n is odd},\sqrt[n]{a^n}=a.\\ \text{Here n = 5 odd}\\ \sqrt[5]{u^5}=u\end{array}$

Part(b) Step 1. Given informaiton

$ⓑ \sqrt[8]{v^8}$

 Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{We use the absolute value to be sure to get the positive root.}\\ \text{Since the index n is even},\sqrt[n]{a^n}=\left|a\right|.\\ \text{Here n = 8 even number}\\ \sqrt[8]{v^8}=\left|v\right|\end{array}$