Q. 183 - Intermediate Algebra

Question

In the following exercises, simplify.

a.$(-2\sqrt{3})\left(3\sqrt{18}\right)$

b.$\left(8\sqrt[3]{4}\right)(-4\sqrt[3]{18})$

Step-by-Step Solution

Answer

On simplification, we get $-18\sqrt{6},-64\sqrt[3]{9}$ respectively

Part (a) Step 1: Given information

Given the expression $(-2\sqrt{3})\left(3\sqrt{18}\right),\left(8\sqrt[3]{4}\right)(-4\sqrt[3]{18})$

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

Simplifying like terms, we get

$$\begin{gathered} (-2\sqrt{3})\left(3\sqrt{18}\right)=(-2.3).(\sqrt{3}.\sqrt{18}) \\ (-2\sqrt{3})\left(3\sqrt{18}\right)=-6.(\sqrt{3}.\sqrt{6}.\sqrt{3}) \\ (-2\sqrt{3})\left(3\sqrt{18}\right)==-6\left(3\sqrt{6}\right) \\ (-2\sqrt{3})\left(3\sqrt{18}\right)=-18\sqrt{6} \end{gathered}$$

Part (b) Step 1: Given information

Given expression $\left(8\sqrt[3]{4}\right)(-4\sqrt[3]{18})$

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

Simplifying, we get

$$\begin{gathered} \left(8\sqrt[3]{4}\right)(-4\sqrt[3]{18})=[8·(-4\left)\right](\sqrt[3]{4}·\sqrt[3]{18}) \\ \left(8\sqrt[3]{4}\right)(-4\sqrt[3]{18})=-32·\sqrt[3]{72} \\ \left(8\sqrt[3]{4}\right)(-4\sqrt[3]{18})=-32·\sqrt[3]{8·9} \\ \left(8\sqrt[3]{4}\right)(-4\sqrt[3]{18})=-32·\sqrt[3]{8}·\sqrt[3]{9} \\ \left(8\sqrt[3]{4}\right)(-4\sqrt[3]{18})=-32·\sqrt[3]{(2{)}^3}·\sqrt[3]{9} \\ \left(8\sqrt[3]{4}\right)(-4\sqrt[3]{18})=-32·2·\sqrt[3]{9} \\ \left(8\sqrt[3]{4}\right)(-4\sqrt[3]{18})=-64\sqrt[3]{9} \end{gathered}$$