How do you evaluate 23543243316?

1 Answer
May 5, 2017

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

Explanation:

First, factor the radicands completely into prime numbers

54=(2)(3)(3)(3)
24=(2)(2)(2)(3)
16=(2)(2)(2)(2)

Since these are cube roots, every perfect cube extracts as a single factor. So, in the case of 54, (3)(3)(3) extracts as 3. The other factors remain inside their respective radicals.

354=332
324=233
316=232

Our expression simplifies as

23543243316=632233632

=233

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.