Q. 193 - Intermediate Algebra

Question

In the following exercises, multiply.

a.$\sqrt{11}(-3+4\sqrt{11})$

b.$\sqrt[4]{3}(\sqrt[4]{54}+\sqrt[4]{18})$

Step-by-Step Solution

Answer

On multiplication, we get $-3\sqrt{11}+44,3\sqrt[4]{2}+\sqrt[4]{54}$ respectively

Part (a) Step 1: Given information

Given the expression $\sqrt{11}(-3+4\sqrt{11})$

Part (a) Step 2: Multiplying the terms and simplifying

Multiplying the terms and simplifying

$$\begin{gathered} \sqrt{11}(-3+4\sqrt{11})=-3\sqrt{11}+4\times 11 \\ \sqrt{11}(-3+4\sqrt{11})=-3\sqrt{11}+44 \end{gathered}$$

Part (b) Step 1: Given information

Given expression $\sqrt[4]{3}(\sqrt[4]{54}+\sqrt[4]{18})$

Part (b) Step 2: Multiplying the terms and simplifying

Multiplying the terms and simplifying, we get

$$\begin{gathered} \sqrt[4]{3}(\sqrt[4]{54}+\sqrt[4]{18})=\sqrt[4]{3}·\sqrt[4]{54}+\sqrt[4]{3}·\sqrt[4]{18} \\ \sqrt[4]{3}(\sqrt[4]{54}+\sqrt[4]{18})=\sqrt[4]{162}+\sqrt[4]{54} \\ \sqrt[4]{3}(\sqrt[4]{54}+\sqrt[4]{18})==\sqrt[4]{81·2}+\sqrt[4]{54} \\ \sqrt[4]{3}(\sqrt[4]{54}+\sqrt[4]{18})=\sqrt[4]{81}·\sqrt[4]{2}+\sqrt[4]{54} \\ \sqrt[4]{3}(\sqrt[4]{54}+\sqrt[4]{18})=\sqrt[4]{(3{)}^4}·\sqrt[4]{2}+\sqrt[4]{54} \\ \sqrt[4]{3}(\sqrt[4]{54}+\sqrt[4]{18})=3·\sqrt[4]{2}+\sqrt[4]{54} \\ \sqrt[4]{3}(\sqrt[4]{54}+\sqrt[4]{18})=3\sqrt[4]{2}+\sqrt[4]{54} \end{gathered}$$