Q. 40 - Intermediate Algebra

Question

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

$ⓐ \sqrt{100y^2} ⓑ -\sqrt{100m^{32}}$

Step-by-Step Solution

Answer

Part(a)$\sqrt{100y^2}=10\left|y\right|$

Part(b)$\sqrt{100m^{32}}=10m^{16}$

Part(a) Step 1. Given information

$ⓐ \sqrt{100y^2}$

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

Step 2. Explanation

$\begin{array}{l}\text{Since;}\\ \Rightarrow 100y^2\\ \Rightarrow \sqrt{100y^2}\\ \Rightarrow 10y^2\\ \text{Since the index n is seven =}\sqrt[n]{a^n}=\left|n\right|\\ \Rightarrow \sqrt{100y^2}=10\left|y\right|\end{array}$

Part(b) Step 1. Given information

$ⓑ -\sqrt{100m^{32}}$

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

Step 2. Explanation

$\begin{array}{l}\text{Since;}\\ \text{I}\Rightarrow =100m^{32}\\ \Rightarrow \sqrt{100m^{32}}\\ \Rightarrow 10m^{16}\\ \text{Since the index n is even =}\sqrt[n]{a^n}=\left|n\right|\\ \Rightarrow \sqrt{100m^{32}}=10m^{16}\end{array}$