### Cube roots

The cube root of a number is the factor that we multiply by itself three times to get that number.

The symbol for cube root is $\sqrt[3]{}$ .

Finding the cube root of a number is the opposite of cubing a number.

**Example:**

$\purpleD3\times \purpleD3\times \purpleD3$ = $\purpleD3^\pink3 = \greenD{27}$

So $\sqrt[\pink3]{\greenD{27}}$ = $\purpleD3$

*Want to learn more about finding cube roots? Check out this video.*

## Finding cube roots

If we can't figure out what factor multiplied by itself three times will result in the given number, we can make a factor tree.

**Example:**

Here is the factor tree for $64$:

So the prime factorization of $64$ is $2\times 2\times 2\times 2\times 2\times 2$.

We're looking for $\sqrt[3]{64}$, so we want to split the prime factors into three identical groups.

Notice that we can rearrange the factors like so:

So $\left(2\times 2\right)^3 = 4^3 = 64$.

So $\sqrt[3]{64}$ is $4$.

## Practice

*Want to try more problems like this? Check out this exercise:*Finding cube roots

*Or this challenge exercise:*Equations with square and cube roots