# How do you simplify 2 cubed root 81 + 3 cubed root 24?

Mar 15, 2018

The answer is $12 \sqrt[3]{3}$ and the solution follows.

#### Explanation:

Look at the values whose cube roots are involved in the problem and determine whether they are perfect cubes or whether they contain factors which are perfect cubes (24 is 3 x 8, and 8 is a perfect cube, and 81 is 3 x 27; 27 is a perfect cube).

This allows you to simplify the problem as shown here:

$2 \sqrt[3]{81} + 3 \sqrt[3]{24}$

$2 \sqrt[3]{27 \times 3} + 3 \sqrt[3]{8 \times 3}$

$2 \left(\sqrt[3]{27} \times \sqrt[3]{3}\right) + 3 \left(\sqrt[3]{8} \times \sqrt[3]{3}\right)$

This step is true because $\sqrt[3]{a \times b} = \sqrt[3]{a} \times \sqrt[3]{b}$
I've put in some brackets in the hope of keeping this clear.

$2 \left(3 \times \sqrt[3]{3}\right) + 3 \left(2 \times \sqrt[3]{3}\right)$

$6 \sqrt[3]{3} + 6 \sqrt[3]{3} = 12 \sqrt[3]{3}$

Mar 15, 2018

$12 \sqrt[3]{3}$

#### Explanation:

$2 \sqrt[3]{81} + 3 \sqrt[3]{24} = 2 \sqrt[3]{27.3} + 3 \sqrt[3]{8.3}$

$= 2.3 \sqrt[3]{3} + 3.2 \sqrt[3]{3} = 6 \sqrt[3]{3} + 6 \sqrt[3]{3} = 12 \sqrt[3]{3}$