Q. 236 - Intermediate Algebra

Question

Simplify:

$\left(3\sqrt[4]{8a^2}\right)\left(\sqrt[4]{12a^3}\right)$

Step-by-Step Solution

Answer

The value of the given expression is $6a\sqrt[4]{6a}$

Step 1. Given information

The given expression is $\left(3\sqrt[4]{8a^2}\right)\left(\sqrt[4]{12a^3}\right)$

Step 2. Simplifying the expression

We know that, 

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

Then

$$\begin{gathered} \left(3\sqrt[4]{8a^2}\right)\left(\sqrt[4]{12a^3}\right) \\ 3\sqrt[4]{8a^2·12a^3} \\ 3\sqrt[4]{96a^5} \\ 3\sqrt[4]{16a^4·6a} \\ 3·2a\sqrt[4]{6a} [\sqrt[4]{16a^4}=2a] \\ 6a\sqrt[4]{6a} \end{gathered}$$