Q. 42 - Intermediate Algebra

Question

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

$ⓐ \sqrt{81x^{36}}ⓑ -\sqrt{25x^2}$

Step-by-Step Solution

Answer

Part(a)$\sqrt{81x^{36}}=9x^{18}$

Part(b)$-\sqrt{25x^2}=-5\left|x\right|$

Part(a) Step 1. Given information

$ⓐ \sqrt{81x^{36}}$

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

Step 2. Explanation

$\begin{array}{l}\text{Since;}\\ =81x^{36}\\ \Rightarrow \sqrt{81x^{36}}\\ \Rightarrow \sqrt{{\left(9x^{18}\right)}^2}\\ \Rightarrow 9x^{18}\\ \text{Since the index n is even =}\sqrt[n]{a^n}=\left|n\right|\\ \Rightarrow \sqrt{81x^{36}}=9x^{18}\end{array}$

Part(b) Step 1. Given information

$ⓑ -\sqrt{25x^2}$

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

Step 2 Explanation

$\begin{array}{l}\text{Since;}\\ \Rightarrow =25x^2\\ \Rightarrow -\sqrt{25x^2}\\ \Rightarrow -5x^2\\ \text{Since the index n is even =}\sqrt[n]{a^n}=\left|n\right|\\ \Rightarrow -\sqrt{25x^2}=-5\left|x\right|\end{array}$