Q. 47 - Intermediate Algebra

Question

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

$ⓐ \sqrt{144x^2{y}^2} ⓑ\sqrt{169w^8{y}^{10}} ⓒ \sqrt[3]{8a^{51}{b}^6}$

Step-by-Step Solution

Answer

Part(a)$\sqrt{144x^2{y}^2}=12\left|xy\right|$

Part(b)$\sqrt{169w^8{y}^{10}}=13w^4\left|y^5\right|$

Part(c) $\sqrt[3]{8a^{51}{b}^6}=2a^{17}{b}^2$

Part(a) Step 1. Given information

$ⓐ \sqrt{144x^2{y}^2}$

Simplify using absolute values as necessary. 

Step 2. Explanation

$\begin{array}{l}\text{Since}\\ {\left(12xy\right)}^2=144x^2{y}^2\\ \Rightarrow \sqrt[]{144x^2{y}^2}\\ \Rightarrow \sqrt{{\left(12xy\right)}^2}\\ \Rightarrow 12\left|xy\right|\end{array}$

Part(b) Step 1. Given information

$ⓑ\sqrt{169w^8{y}^{10}}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Since,}\\ \Rightarrow {\left(13w^4{y}^5\right)}^2=169w^8{y}^{10}\\ \Rightarrow \sqrt[]{169w^8{y}^{10}}\\ \Rightarrow \sqrt[]{{\left(13w^4{y}^5\right)}^2}\\ \Rightarrow 13w^4\left|y^5\right|\end{array}$

Part(c) Step 1. Given information

$ⓒ \sqrt[3]{8a^{51}{b}^6}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Since,}\\ \Rightarrow {\left(2a^{17}{b}^2\right)}^3\Rightarrow =8a^{51}{b}^6\\ \Rightarrow \sqrt[3]{8a^{51}{b}^6}\\ \Rightarrow \sqrt[3]{{\left(2a^{17}{b}^2\right)}^3}\\ \Rightarrow 2a^{17}{b}^2\end{array}$