How do you simplify #root3(96 )#?

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Answer 1 · 2017-02-12T21:59:49

#2root(3)(12)#

As this is a cube root you are looking for cubed numbers that are factors of 96.

If you are ever unsure draw a quick sketch of a prime factor tree.

Tony B

From this observe that the group of 3 prime numbers that are the same is: #2xx2xx2#. Sometimes you will get more (or less)

The remainder is #2xx2xx3 =12#

So we write our expression as: #root(3)(2^3xx12)#

We can take the #2^3# outside the root where it becomes just 2 giving

#2root(3)(12)#