If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Middle school math (India)>Unit 6

Lesson 3: Cube roots

# Cube root of a non-perfect cube

Created by Sal Khan.

## Want to join the conversation?

• I am so very lost.
I have prime factorization down but this video leaves me utterly confused about how to find the cube root. The hints in the problems aren't very helpful. I do not understand how to go from prime factors to the cube root of non-perfect numbers. Please help!
• You prime factorize the number then what you do is group the numbers appearing three times
like 7 in above video.group the other numbers appearing in times which are not multiples of three (2 and 5 in above example). multiply them and write them in the form cuberoot of
'multiplied number" (here 10 i.e 2*5).At last take the number you grouped first(number appearing three times) and write in form "X x cuberoot of y" where X=first grouped num..... y=second grouped num............ x=multiplied by
• I understand the method, but I spot two problems:

* won't different people get different answers depending upon which factors they try first?
* how do we know that the final surd form is the simplest?

Or is this just an illustration of factoring?

Thank you.
• Well if you tried using different factors to start with, you will get the same answers eventually at the end when it is fully simplified. So in this example, you can start out by dividing by 7,5, or 49, for example, and the answer at the end for all three is still the same. You can tell when the final form is the simplest when all the numbers you have left are prime numbers or in other words they can't be broken down further (e.g. 2,3,5,7,11, etc.) Knowing what the prime numbers are comes with practice.
• What are imaginary numbers? How do they work?
• What the easiest way to do a cube root with a non-perfect cube
• Are there other ways (other than prime factorization) to find the cube root of a number?
(1 vote)
• I think you can do the factor tree but not 100% so stick with this for now ...
• i am kinda lost please explain what sal means
2. 7, 7 and 7 can be said as the cube root of 7*7*7.
3. 2 and 5 cannot be grouped so we can say it as the cube root of 10 (multiply them.)
4. Multiply them.
(1 vote)
• I was wondering, what method can one use to calculate the cube root of a prime number without a calculator? for example I am supposed to know how to calculate 2 to the power 1/3 without using a calculator.
• Nope, these sort of things need a calculator. Without one your answer are normally expected stay 2^1/3. Now, if it wasn't a prime number you could do more with it.