Q. 232 - Intermediate Algebra

Question

Simplify:

$\left(4\sqrt{21x^5}\right)\left(2\sqrt{6x^3}\right)$

Step-by-Step Solution

Answer

The value of the given expression is $48x^2\sqrt{2}$

Step 1. Given information

The given expression is $\left(4\sqrt{21x^5}\right)\left(2\sqrt{6x^3}\right)$

Step 2. Simplifying the expression

We know that,

 $\left(\sqrt[n]{a}\right)\left(\sqrt[n]{b}\right)=\left(\sqrt[n]{ab}\right)$

Then,

$$\begin{gathered} \left(4\sqrt{12x^5}\right)\left(2\sqrt{6x^3}\right) \\ 4·2\left(\sqrt{12x^5·6x^3}\right) \\ 8\left(\sqrt{72x^8}\right) \left[a^b·a^c=a^{a+c}\right] \\ 8\left(\sqrt{36·2·x^8}\right) \\ 8\left(\sqrt{{\left(6x\right)}^2·2}\right) \\ 8·6x^2\sqrt{2} [\sqrt{36x^4}=6x^2] \\ 48x^2\sqrt{2} \end{gathered}$$