Q. 49 - Intermediate Algebra

Question

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

$ⓐ \sqrt{121a^2{b}^2} ⓑ \sqrt{9c^8{d}^{12}} ⓒ \sqrt[3]{64x^{15}{y}^{66}}$

Step-by-Step Solution

Answer

Part(a)$\sqrt{121a^2{b}^2}=11\left|ab\right|$

Part(b)$\sqrt{9c^8{d}^{12}}=3c^4{d}^6$

Part(c)$\sqrt[3]{64x^{15}{y}^{66}}=4x^5{y}^{22}$

Part(a) Step 1. Given information

$ⓐ \sqrt{121a^2{b}^2}$

 Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Since}\\ \Rightarrow {\left(11ab\right)}^2=121a^2{b}^2\\ \Rightarrow \sqrt[]{121a^2{b}^2}\\ \Rightarrow \sqrt{{\left(11ab\right)}^2}\\ \Rightarrow 11\left|ab\right|\end{array}$

Part(b) Step 1. Given information

$ⓑ \sqrt{9c^8{d}^{12}}$

 Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Since,}\\ \Rightarrow {\left(3c^4{d}^6\right)}^2=9c^8{d}^{12}\\ \Rightarrow \sqrt[]{9c^8{d}^{12}}\\ \Rightarrow \sqrt[]{{\left(3c^4{d}^6\right)}^2}\\ \Rightarrow 3c^4{d}^6\end{array}$

Part(c) Step 1. Given information

$ⓒ \sqrt[3]{64x^{15}{y}^{66}}$

 Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l}\text{Since,}\\ \Rightarrow {\left(4x^5{y}^{22}\right)}^3=64x^{15}{y}^{66}\\ \Rightarrow \sqrt[3]{64x^{15}{y}^{66}}\\ \Rightarrow \sqrt[3]{{\left(4x^5{y}^{22}\right)}^3}\\ \Rightarrow 4x^5{y}^{22}\end{array}$