Q. 191 - Intermediate Algebra

Question

In the following exercises, multiply.

a.$\sqrt{7}(5+2\sqrt{7})$

b.$\sqrt[3]{6}(4+\sqrt[3]{18})$

Step-by-Step Solution

Answer

On multiplication, we get $14+5\sqrt{7},4\sqrt[3]{6}+3\sqrt[3]{4}$ respectively

Part (a) Step 1: Given information

Given the expression $\sqrt{7}(5+2\sqrt{7}),\sqrt[3]{6}(4+\sqrt[3]{18})$

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

Multiplying the terms and simplifying, we get

$$\begin{gathered} \sqrt{7}(5+2\sqrt{7})=5\sqrt{7}+2\times 7 \\ \sqrt{7}(5+2\sqrt{7})=5\sqrt{7}+14 \end{gathered}$$

Part (b) Step 1: Given information

Given expression $\sqrt[3]{6}(4+\sqrt[3]{18})$

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

Multiplying the terms and simplifying, we get

$$\begin{gathered} \sqrt[3]{6}(4+\sqrt[3]{18})=4·\sqrt[3]{6}+\sqrt[3]{6}·\sqrt[3]{18} \\ \sqrt[3]{6}(4+\sqrt[3]{18})=4\sqrt[3]{6}+\sqrt[3]{108} \\ \sqrt[3]{6}(4+\sqrt[3]{18})=4\sqrt[3]{6}+\sqrt[3]{27.4} \\ \sqrt[3]{6}(4+\sqrt[3]{18})=4\sqrt[3]{6}+\sqrt[3]{27}·\sqrt[3]{4} \\ \sqrt[3]{6}(4+\sqrt[3]{18})=4\sqrt[3]{6}+\sqrt[3]{(3{)}^3}·\sqrt[3]{4} \\ \sqrt[3]{6}(4+\sqrt[3]{18})=4\sqrt[3]{6}+3\sqrt[3]{4} \end{gathered}$$