Q. 186 - Intermediate Algebra

Question

In the following exercises, simplify.

a.$(-2\sqrt{7})(-2\sqrt{14})$

b.$(-3\sqrt[4]{8})(-5\sqrt[4]{6})$

Step-by-Step Solution

Answer

On multiplication, we get $28\sqrt{2},30\sqrt[4]{3}$ respectively

Part (a) Step 1: Given information

Given the expression $(-2\sqrt{7})(-2\sqrt{14})$

Part (a) Step 2:

Multiplying the terms and simplifying, we get

$$\begin{gathered} (-2\sqrt{7})(-2\sqrt{14})=\left[\right(-2)·(-2\left)\right](\sqrt{7}·\sqrt{14}) \\ (-2\sqrt{7})(-2\sqrt{14})=4[\sqrt{7}.\sqrt{7}.\sqrt{2}] \\ (-2\sqrt{7})(-2\sqrt{14})=28\sqrt{2} \end{gathered}$$

Part (b) Step 1: Given information

Given expression $(-3\sqrt[4]{8})(-5\sqrt[4]{6})$

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

Multiplying, we get

$$\begin{gathered} (-3\sqrt[4]{8})(-5\sqrt[4]{6})=\left[\right(-3)·(-5\left)\right](\sqrt[4]{8}·\sqrt[4]{6}) \\ (-3\sqrt[4]{8})(-5\sqrt[4]{6})=15·\sqrt[4]{48} \\ (-3\sqrt[4]{8})(-5\sqrt[4]{6})=15·\sqrt[4]{16·3} \\ (-3\sqrt[4]{8})(-5\sqrt[4]{6})=15·\sqrt[4]{16}·\sqrt[4]{3} \\ (-3\sqrt[4]{8})(-5\sqrt[4]{6})=15·\sqrt[4]{(2{)}^4}·\sqrt[4]{3} \\ (-3\sqrt[4]{8})(-5\sqrt[4]{6})=15·2·\sqrt[4]{3} \\ (-3\sqrt[4]{8})(-5\sqrt[4]{6})=30\sqrt[4]{3} \end{gathered}$$