Q. 192 - Intermediate Algebra

Question

In the following exercises, multiply.

a.$\sqrt{11}(8+4\sqrt{11})$

b.$\sqrt[3]{3}(\sqrt[3]{9}+\sqrt[3]{18})$

Step-by-Step Solution

Answer

On multiplication, we get $8\sqrt{11}+44,3+3\sqrt[3]{2}$ respectively

Part (a) Step 1: Given information

Given the expression $\sqrt{11}(8+4\sqrt{11})$

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

Multiplying the terms and simplifying

$$\begin{gathered} \sqrt{11}(8+4\sqrt{11})=8\sqrt{11}+4\times 11 \\ \sqrt{11}(8+4\sqrt{11})=8\sqrt{11}+44 \end{gathered}$$

Part (b) Step 1: Given information

Given expression $\sqrt[3]{3}(\sqrt[3]{9}+\sqrt[3]{18})$

Part (b): Multiplying the terms and simplifying

Multiplying the terms and simplifying, we get

$$\begin{gathered} \sqrt[3]{3}(\sqrt[3]{9}+\sqrt[3]{18})=\sqrt[3]{3}·\sqrt[3]{9}+\sqrt[3]{3}·\sqrt[3]{18} \\ \sqrt[3]{3}(\sqrt[3]{9}+\sqrt[3]{18})=\sqrt[3]{27}+\sqrt[3]{54} \\ \sqrt[3]{3}(\sqrt[3]{9}+\sqrt[3]{18})=\sqrt[3]{27}+\sqrt[3]{27.2} \\ \sqrt[3]{3}(\sqrt[3]{9}+\sqrt[3]{18})=\sqrt[3]{27}+\sqrt[3]{27}·\sqrt[3]{2} \\ \sqrt[3]{3}(\sqrt[3]{9}+\sqrt[3]{18})=\sqrt[3]{(3{)}^3}+\sqrt[3]{(27{)}^3}·\sqrt[3]{2} \\ \sqrt[3]{3}(\sqrt[3]{9}+\sqrt[3]{18})=3+3·\sqrt[3]{2} \\ \sqrt[3]{3}(\sqrt[3]{9}+\sqrt[3]{18})=3+3\sqrt[3]{2} \end{gathered}$$