# How do you evaluate #2 root3 { 54} - \root[ 3] { 24} - 3\root [ 3] { 16}#?

##### 1 Answer

May 5, 2017

Simplify all of the radicals first, then combine like terms.

#### Explanation:

First, factor the radicands completely into prime numbers

Since these are cube roots, every perfect cube extracts as a single factor. So, in the case of 54,

Our expression simplifies as

Observe that cube roots of 2 and cube roots of 3 would not have combined with one another. That fact is not important in this problem, though, since all of the cube roots of 2 have canceled out to zero.