Q. 220 - Intermediate Algebra

Question

Simplify: 

$\sqrt[3]{24}+\sqrt[3]{81}$

Step-by-Step Solution

Answer

The value of the given expression is $5\sqrt[3]{3}.$

Step 1. Given Information

The given expression is

$\sqrt[3]{24}+\sqrt[3]{81}.$

Step 2. Simplify the radicals

Like radicals can be added or subtracted so,

$$\begin{gathered} \sqrt[3]{24}+\sqrt[3]{81} \\ =\sqrt[3]{8·3}+\sqrt[3]{27·3} \\ =\sqrt[3]{{\left(2\right)}^3}·\sqrt[3]{3}+\sqrt[3]{{\left(3\right)}^3}·\sqrt[3]{3} \\ =2·\sqrt[3]{3}+3·\sqrt[3]{3} \\ =5\sqrt[3]{3} \end{gathered}$$