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# Worked example: Cube root of a negative number

Learn how to find the cube root of -512. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• i still do not get it :( please explain more, for example where did he get the 2's?
• I find it easiest just to Guess and Check....What number cubed equals -512? I find people start to memorize the common ones after a bit.
• How do i get the cube root of a number like 4?
• The cube root won't be an exact number, if that's what you're asking.

To get an idea of what it might be,
4 is found in between 1 and 8
This means that the cube root of 4 will be in between cube root of 1 and cube root of 8, or in other words, between 1 and 2.
4 is closer to 1 than 8 (4-1=3 while 8-4=4). so the cube root of 4 will be a number in between 1 and 1.5
• the cube root does not have to be perfect?
• That is true just like square roots. Any whole number that is not 1, 8, 27, 64, 125 ... is not a perfect cube.
• How to simplify the cube root of 9317 ... any ideas?
• The simplified cube root of that number is 11 3√ 7
• Hang on a second... at , how is the cube root of -1 = -1? Wouldn't it be -i?
• No because -1 x -1 x-1 = -1. When three negatives are multiplied together 2 of them cancel out, but on is left so no there is no change to the sign.
• 2x3=6 not 8 rite?
• 2 x 3 can either be thought of as 2 + 2 + 2 or as 3 + 3. Or stating that another way, 2 groups of 3 items or 3 groups that each have 2 items and it does equal 6.
To cube something is to multiply it by itself, 2 x 2 x 2 = 4 x 2 = 8. It is written 2^3 = 8
• At , couldn't Sal have stop factoring at 64 since 8x8=64?
• No, because 8 isn't a prime number. when doing prime factorization, you have to factor until everything is prime.
• i has a big question.
HOW DO YOU FIND CUBE roots?
• OK, a SQUARE ROOT means find the number that when you multiply it by itself, you get a certain number. Like the square root of 9 is 3 because 3*3=9.

CUBE ROOTS work the same way, but you're looking for a number that when you multiply it by itself twice, you get a certain number. Like the cube root of 8 is 2 because 2*2*2=8

The cube root of 125 is 5 because 5*5*5=125
• Can someone please explane this to me this is hard
• First you do the prime factorization then you make three identical groups of the final numbers. Finally you multiply the numbers together in those groups. This might not help it is my first reply. :(
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀
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