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## 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

CCSS.Math:

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 cube root of, end cube root .

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

**Example:**

start color #7854ab, 3, end color #7854ab, times, start color #7854ab, 3, end color #7854ab, times, start color #7854ab, 3, end color #7854ab = start color #7854ab, 3, end color #7854ab, start superscript, start color #ff00af, 3, end color #ff00af, end superscript, equals, start color #1fab54, 27, end color #1fab54

So root, start index, start color #ff00af, 3, end color #ff00af, end index = start color #7854ab, 3, end color #7854ab

*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 cube root of, 64, end cube root, so we want to split the prime factors into three identical groups.

Notice that we can rearrange the factors like so:

So left parenthesis, 2, times, 2, right parenthesis, cubed, equals, 4, cubed, equals, 64.

So cube root of, 64, end cube root 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?(15 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.(2 votes)

- I get it now cuz when me teacher explains it she makes it really complicated(15 votes)
- But (-2)*(-2)*(2) also equals 8.

So aren’t there then two values for the cubed root of 8: 2 and -2?(2 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!(6 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(2 votes)

- I don’t understand their answer for the last question of the practice. They give no explanation. Why can’t -7 be a solution to plus or minus cube root of 343?

They put the plus and minus in front of the square root for 49 (which I understand) but why can’t you have it in front of the cube root of 343, why not? They don’t explain.(2 votes)- (-7)^3 = -343.

-7*-7*-7 = -343, if we multiply a negative by itself 3 times, you get negative.(2 votes)

- Is there an easy way to solve cubed roots besides memorization? like is there some sort of trick or something?(3 votes)
- I don't understand the problem: Finding the cube root of 64 to the 3 power? Doesn't make sense.(2 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!(3 votes)

- Good Question

How do you figure out large cube root questions without guessing and checking?(3 votes) - Is there some trick to the factor tree to make this work? For 216 my factor tree was 3x72 and then 2x36 and then 6x6 and then 2x3. I actually had to break that 6 into a 2x3 to make the factor trick work. Am I supposed to be going for the smallest factors? Sal didn't specify, from what I recall.(3 votes)
- Yes, you are supposed to use the smallest notation.

Also, you had to change 6 into 2*3 because 6 is not a prime number. You are supposed to change everything into prime numbers.(1 vote)

- Is there a shorter way to do this type of algebra? Is it easy?(1 vote)