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Course: Pre-algebra > Unit 11
Lesson 1: Square roots & cube roots- Intro to square roots
- Square roots of perfect squares
- Square roots
- Intro to cube roots
- Cube roots
- Worked example: Cube root of a negative number
- Equations with square roots & cube roots
- Square root of decimal
- Roots of decimals & fractions
- Equations with square roots: decimals & fractions
- Dimensions of a cube from its volume
- Square and cube challenge
- Square roots review
- Cube roots review
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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 .
Finding the cube root of a number is the opposite of cubing a number.
Example:
So =
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 :
So the prime factorization of is .
We're looking for , so we want to split the prime factors into three identical groups.
Notice that we can rearrange the factors like so:
So .
So is .
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
Want to join the conversation?
- How do you figure out large cube root questions without guessing and checking?(29 votes)
- 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.(16 votes)
- Is there an easier method?(5 votes)
- A calculator 🙃(37 votes)
- But (-2)*(-2)*(2) also equals 8.
So aren’t there then two values for the cubed root of 8: 2 and -2?(3 votes)- 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!(14 votes)
- I don't understand the problem: Finding the cube root of 64 to the 3 power? Doesn't make sense.(4 votes)
- 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!(8 votes)
- i dont understand this, how do i do it? (i didnt learn this)(2 votes)
- 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.(8 votes)
- Is there an easier way to find the cube root(4 votes)
- Is there any way you can find cube roots in your head or any way like doing long division?(5 votes)
- 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)?(2 votes)
- No, because when you cube something, you multiply it by itself three times, 4*4*4=64(6 votes)
- i dont get it(3 votes)
- If you tell me what particular part you don't understand, i might be able to help you.(3 votes)
- Are there any other roots such as 4_/x (4D root of x)?(4 votes)
- You absolutely can take any nth root of x (n > 0). However those aren't common, since we live in 3 spatial dimensions after all.
Later on, you will even see how roots are related to the exponent!
Happy learning.(2 votes)