Guided Example #2 - Radical Functions

Simplify. $2 \sqrt[3]{3 a^{4}} - 3 a \sqrt[3]{81 a}$

a. $- 7 a \sqrt[3]{3 a}$
b. $- a \sqrt[3]{3 a}$
c. $- 7 \sqrt[3]{3 a}$
d. None of the above

The correct answer is A. To see why, view each of the steps below.

Step 1

First simplify each term by writing the radicands as the product of a perfect third powers and factors that do not contain perfect third powers. Then combine like terms by using the Distributive Property.

Step 2

And

$3 a \sqrt[3]{81 a} = 3 a \sqrt[3]{27 .3 a} = 3 a \sqrt[3]{27} . \sqrt[3]{a} = 3 a (3) \sqrt[3]{a} = 9 a \sqrt[3]{a}$

Step 3

Therefore,

$2 \sqrt[3]{3 a^{4}} - 3 a \sqrt[3]{81 a} = 2 a \sqrt[3]{a} - 9 a \sqrt[3]{a} = - 7 \sqrt[3]{a}$

All Steps

And

$3 a \sqrt[3]{81 a} = 3 a \sqrt[3]{27 .3 a} = 3 a \sqrt[3]{27} . \sqrt[3]{a} = 3 a (3) \sqrt[3]{a} = 9 a \sqrt[3]{a}$

Therefore,

$2 \sqrt[3]{3 a^{4}} - 3 a \sqrt[3]{81 a} = 2 a \sqrt[3]{a} - 9 a \sqrt[3]{a} = - 7 \sqrt[3]{a}$