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# Cube roots review

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 $\sqrt[3]{\phantom{A}}$ .
Finding the cube root of a number is the opposite of cubing a number.
Example:
$3×3×3$ = ${3}^{3}=27$
So $\sqrt[3]{\phantom{A}27}$ = $3$

## 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:
$\sqrt[3]{\phantom{A}64}=\text{?}$
Here is the factor tree for $64$:
So the prime factorization of $64$ is $2×2×2×2×2×2$.
We're looking for $\sqrt[3]{\phantom{A}64}$, so we want to split the prime factors into three identical groups.
Notice that we can rearrange the factors like so:
$64=2×2×2×2×2×2=\left(2×2\right)×\left(2×2\right)×\left(2×2\right)$
So ${\left(2×2\right)}^{3}={4}^{3}=64$.
So $\sqrt[3]{\phantom{A}64}$ is $4$.

## Practice

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

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

## Want to join the conversation?

• How do you figure out large cube root questions without guessing and checking?
• Sometimes what I do is rememebr simple pefect squares. For example, 4=64, 3=27.Sometimes the thing that works the best is just multiplying the number you are figure out by the given factor.
• Is there an easier method?
• A calculator 🙃
• But (-2)*(-2)*(2) also equals 8.
So aren’t there then two values for the cubed root of 8: 2 and -2?
• But -2 and 2 aren't the same number, so you aren't technically cubing it, since cubes are the SAME number multiplied three times. Hope this helped!
• I don't understand the problem: Finding the cube root of 64 to the 3 power? Doesn't make sense.
• The process of taking the cube root is the reverse of the process of taking a number to the 3 power. So these processes undo each other; therefore, the answer is just 64.

Have a blessed, wonderful day!
• i dont understand this, how do i do it? (i didnt learn this)
• cube roots are inverses of cubic function, so if 3^3=27, the cube rott of 27=3. If you prime factor 27, you get 27=9*3=3*3*3, so on cube roots, you need three of the same number multiplied together which will come out as a single 3.
5^3=125, so cube root of (125)=cube root (5^3) = 5.
• Is there an easier way to find the cube root
• Is there any way you can find cube roots in your head or any way like doing long division?
• What I do is using my own knowledge. For example, I'm trying to find 3v729 and I know that 8^3 is 512, so the answer must be bigger than 8. Then, I realized it might be 9 so I did the multiplication, and turns out I'm right. It's basically an estimation. I hope this helps!
(1 vote)
• So if the question is the cubed root of 64, would that mean (8*8=64) = (64/3)?