Q. 590 - Intermediate Algebra

Question

In the following exercises, simplify. Assume all variables are positive.

$\sqrt[3]{4}\left(\sqrt[3]{16}-\sqrt[3]{6}\right)$

Step-by-Step Solution

Answer

The simplification of the expression is $4-2\sqrt[3]{3}$

Step 1. Given Information

We have $\sqrt[3]{4}\left(\sqrt[3]{16}-\sqrt[3]{6}\right)$

Step 2. Multiply by distributive property

$$\begin{gathered} \sqrt[3]{4}\left(\sqrt[3]{16}-\sqrt[3]{6}\right) \\ =\sqrt[3]{4}\sqrt[3]{16}-\sqrt[3]{4}\sqrt[3]{6} \end{gathered}$$

Step 3. Simplify the expression

$$\begin{gathered} =\sqrt[3]{64}-\sqrt[3]{24} \\ =\sqrt[3]{4\times 4\times 4}-\sqrt[3]{2\times 2\times 2\times 3} \\ =4-2\sqrt[3]{3} \end{gathered}$$