Q. 180 - Intermediate Algebra

Question

In the following exercises, simplify.

a.$\sqrt{96d^9}-\sqrt{24d^9}$

b.$5\sqrt[4]{243s^6}+2\sqrt[4]{3s^6}$

Step-by-Step Solution

Answer

On simplification, we get $2d^4\sqrt{6d},17\sqrt[4]{3s^6}$ respectively

Part (a) Step 1: Given information

Given the expression $\sqrt{96d^9}-\sqrt{24d^9}$

Part (a) Step 2: Simplifying the radical and combine like terms

Simplifying radical and combining, we get

$$\begin{gathered} \sqrt{96d^9}-\sqrt{24d^9}=\sqrt{16d^8·6d}-\sqrt{4d^8·6d} \\ \sqrt{96d^9}-\sqrt{24d^9}=\sqrt{16d^8}·\sqrt{6d}-\sqrt{4d^8}·\sqrt{6d} \\ \sqrt{96d^9}-\sqrt{24d^9}=\sqrt{{\left(4d^4\right)}^2}·\sqrt{6d}-\sqrt{{\left(2d^4\right)}^2}·\sqrt{6d} \\ \sqrt{96d^9}-\sqrt{24d^9}=4d^4\sqrt{6d}-2d^4\sqrt{6d} \\ \sqrt{96d^9}-\sqrt{24d^9}=2d^4\sqrt{6d} \end{gathered}$$

Part (b) Step 1: Given information

Given expression $5\sqrt[4]{243s^6}+2\sqrt[4]{3s^6}$

Part (b) Step 2: Simplifying the radical and combine like terms

Simplifying like terms, we get

$$\begin{gathered} 5\sqrt[4]{243s^6}+2\sqrt[4]{3s^6}=5\sqrt[4]{81·3s^6}+2\sqrt[4]{3s^6} \\ 5\sqrt[4]{243s^6}+2\sqrt[4]{3s^6}=5·\sqrt[4]{81}·\sqrt[4]{3s^6}+2\sqrt[4]{3s^6} \\ 5·\sqrt[4]{81}·\sqrt[4]{3s^6}+2\sqrt[4]{3s^6}=5·\sqrt[4]{(3{)}^4}·\sqrt[4]{3s^6}+2\sqrt[4]{3s^6} \\ 5·\sqrt[4]{81}·\sqrt[4]{3s^6}+2\sqrt[4]{3s^6}=15\sqrt[4]{3s^6}+2\sqrt[4]{3s^6} \\ 5·\sqrt[4]{81}·\sqrt[4]{3s^6}+2\sqrt[4]{3s^6}=17\sqrt[4]{3s^6} \end{gathered}$$