Q. 185 - Intermediate Algebra

Question

In the following exercises, simplify.

a.$\left(5\sqrt{6}\right)(-\sqrt{12})$

b.$(-2\sqrt[4]{18})(-\sqrt[4]{9})$

Step-by-Step Solution

Answer

On multiplication, we get $-30\sqrt{2},6\sqrt[4]{2}$ respectively

Part (a) Step 1: Given information

Given the expression $\left(5\sqrt{6}\right)(-\sqrt{12}),(-2\sqrt[4]{18})(-\sqrt[4]{9})$

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

Multiplying the terms and simplifying, we get, we get

$$\begin{gathered} \left(5\sqrt{6}\right)(-\sqrt{12})=(5.-1)(\sqrt{6}.\sqrt{12}) \\ \left(5\sqrt{6}\right)(-\sqrt{12})=-5(\sqrt{6}.\sqrt{6}.\sqrt{2}) \\ \left(5\sqrt{6}\right)(-\sqrt{12})=-5\left(6\sqrt{2}\right) \\ \left(5\sqrt{6}\right)(-\sqrt{12})=-30\sqrt{2} \end{gathered}$$

Part (b) Step 1: Given information

Given expression $(-2\sqrt[4]{18})(-\sqrt[4]{9})$

Part (b) Step 2: Multiplying and simplifying

Multiplying, we get

$$\begin{gathered} (-2\sqrt[4]{18})(-\sqrt[4]{9})=\left[\right(-2)·(-1\left)\right](\sqrt[4]{18}·\sqrt[4]{9}) \\ (-2\sqrt[4]{18})(-\sqrt[4]{9})=2·\sqrt[4]{162} \\ (-2\sqrt[4]{18})(-\sqrt[4]{9})=2·\sqrt[4]{81·2} \\ (-2\sqrt[4]{18})(-\sqrt[4]{9})=2·\sqrt[4]{81}·\sqrt[4]{2} \\ (-2\sqrt[4]{18})(-\sqrt[4]{9})=2·\sqrt[4]{(3{)}^4}·\sqrt[4]{2} \\ (-2\sqrt[4]{18})(-\sqrt[4]{9})=2·3·\sqrt[4]{2} \\ (-2\sqrt[4]{18})(-\sqrt[4]{9})=6\sqrt[4]{2} \end{gathered}$$