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 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

$2root(3)(12)$

How do you simplify root3(96 )root3(96 )?