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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!
• So if the question is the cubed root of 64, would that mean (8*8=64) = (64/3)?
• No, because when you cube something, you multiply it by itself three times, 4*4*4=64
• 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 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!
• i dont get it
• If you tell me what particular part you don't understand, i might be able to help you.
• Is there an easier way to find the cube root
• I was supposed to factor out 216 but when I started with 2, I ended up with 2,2,2,3,9 and that doesn't work. I only got the right answer when I started with six. Why does 2 not work?
• 2 works! Let's try it.
We factor out a 2 from 216. We get 108
We factor out a 2 from 108. We get 54
We factor out a 2 from 54. We get 27
We factor out a 3 from 27. we get 9
We factor out a 3 from 9. We get 3
We factor out a 3 from 3. We get 1

Answer- 2, 2, 2, 3, 3, 3
Check- 2 × 2 × 2 × 3 × 3 × 3 = 216!
And we got it righty right!
Perhaps you did the Check wrong.