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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 $\sqrt[3]{\phantom{A}}$ .

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

**Example:**

So $\sqrt[{3}]{\phantom{A}{27}}$ = ${3}$

*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 $\sqrt[3]{\phantom{A}64}$ , so we want to split the prime factors into three identical groups.

Notice that we can rearrange the factors like so:

So ${(2\times 2)}^{3}={4}^{3}=64$ .

So $\sqrt[3]{\phantom{A}64}$ 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

## Want to join the conversation?

- How do you figure out large cube root questions without guessing and checking?(25 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 🙃(27 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!(12 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!(7 votes)

- So if the question is the cubed root of 64, would that mean (8*8=64) = (64/3)?(3 votes)
- No, because when you cube something, you multiply it by itself three times, 4*4*4=64(6 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 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!(2 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.(4 votes)

- Is there an easier way to find the cube root(4 votes)
- 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?(3 votes)
- 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.

Well you have to factor 9 also in your answer- 2,2,2,3,9

9 can be factored as 3 × 3

So your answer is written as 2, 2, 2, 3, 3, 3(5 votes)