# Cube roots review

CCSS Math: 8.EE.A.2
Review cube roots, and try some practice problems.

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

## 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:
$\Large{\sqrt[3]{64} = \text{?}}$
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:
$64 = 2\times 2\times 2\times 2\times 2\times 2 = \left(2\times 2\right)\times\left(2\times 2\right)\times\left(2\times 2\right)$
So $\left(2\times 2\right)^3 = 4^3 = 64$.
So $\sqrt[3]{64}$ is $4$.

## Practice

Problem 1
$\Large{\sqrt[3]{125} = \text{?}}$

Want to try more problems like this? Check out this exercise: Finding cube roots
Or this challenge exercise: Equations with square and cube roots