Q. 230 - Intermediate Algebra

Question

Simplify:

$\left(4\sqrt{6}\right)\left(-\sqrt{18}\right)$

Step-by-Step Solution

Answer

The value of the given expression is $-24\sqrt{3}$

Step 1. Given information

The given expression is:

$\left(4\sqrt{6}\right)\left(-\sqrt{18}\right)$

Step 2. Simplifying the expression

We know that,

 $\sqrt[n]{a}·\sqrt[n]{b}=\sqrt[n]{ab}$

Then,

$$\begin{gathered} \left(4\sqrt{6}\right)\left(-\sqrt{18}\right) \\ -4\left(\sqrt{6·18}\right) \\ -4\sqrt{108} \\ -4\sqrt{36·3} \\ -4·6\sqrt{3} [\sqrt{36}=6] \\ -24\sqrt{3} \end{gathered}$$