Q. 239 - Intermediate Algebra

Question

In the following exercises, multiply.

$\sqrt[3]{3}(2\sqrt[3]{9}+\sqrt[3]{18})$

Step-by-Step Solution

Answer

The multiplication of $\sqrt[3]{3}(2\sqrt[3]{9}+\sqrt[3]{18})$ is $6+3\sqrt[3]{2}$

Step 1. Given

An expression $\sqrt[3]{3}(2\sqrt[3]{9}+\sqrt[3]{18})$

To multiply the numbers.

Step 2. Multiply the expression

Multiply the expressions since they are like terms.

$\sqrt[3]{3}(2\sqrt[3]{9}+\sqrt[3]{18})=2\sqrt[3]{3\times 9}+\sqrt[3]{3\times 18}$

                            $=2\sqrt[3]{27}+\sqrt[3]{54}$

Step 3. Simplify the expression

$\sqrt[3]{3}(2\sqrt[3]{9}+\sqrt[3]{18})=2\sqrt[3]{3^3}+\sqrt[3]{2}\sqrt[3]{27}$

                            $=2\sqrt[3]{3^3}+\sqrt[3]{2}\sqrt[3]{3^3}$

                            $=6+3\sqrt[3]{2}$