Question

Select the correct answer.
Simplify the expression

Answer 1

Answer: A

Explanation:

Since multiplication is the only operation under the radical, you can apply the root to each term. Im not sure if I worded that correctly, but ill hopefully explain correctly.

First we need to take the cubed root of 648. This number doesn't have a perfect root, but it can be simplified. 648 is the same as 216*3, and 216 has a perfect cubed root of 6. So we can bring the 6 outside of the radical

`3x*6\sqrt[3]{3x^4y^8}=18x\sqrt[3]{3x^4y^8}`

The next step is simplifying the variables, which is the easiest part. Just split them up into multiples of 3, again poor explanation but Ill show what I mean.

`18x\sqrt[3]{3x^3xy^3y^3y^2}`

The cubed root and the cubed power will cancel and can be brought outside the radical
`18x*xy^2\sqrt[3]{2xy^2} =18x^2y^2\sqrt[3]{3xy^2}`