# How do you simplify root3(96 )?

Feb 12, 2017

$2 \sqrt[3]{12}$

#### Explanation:

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.

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

The remainder is $2 \times 2 \times 3 = 12$

So we write our expression as: $\sqrt[3]{{2}^{3} \times 12}$

We can take the ${2}^{3}$ outside the root where it becomes just 2 giving

$2 \sqrt[3]{12}$