Can a Cubed Root Be Negative?

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At one point or another you may perform a mathematical equation and be unsure of the answer. Find out if a cubed root can be negative with help from a mathematics educator in this free video clip.

Part of the Video Series: Mathematics Lessons
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Video Transcript

Hi, I'm Jimmy Chang, and we're here to answer the question, can a cube's root be negative? Now, the short answer to that is, yes. Because a square root can't be negative, because you cannot have a real number squared and give you a negative result. But for a cubed root, it's a little bit different, because of the cube root structure. So, here's a few illustrations to help you. Now, just to help you recap, cube root is a radical with a three, kind of embedded here. And let's suppose, you want to find the cube root of negative eight. Now, what you've got to think about is, this. Can you have a number raised to third power, or multiplied by itself, three times, to give you negative eight. And the answer to that is, yes. That number being negative two, because if you have negative two, multiplied by itself, three times, you will get negative eight. Now, here's another example. Suppose you want to find the cube root of negative 64. Now, you have to ask yourself the m question. Is there a number multiplied by itself three times, or raised to third power, that'll give you negative 64. And the question, the answer is, yes, that number being negative four. Because if you take negative four, multiplied by itself, three times, you'll get negative 64. In both instances, cube roots of negative numbers, will always be negative. Which is perfectly fine, because it's a cube root. Now, if you have something unusual such as he cube root of negative 15, that's not going to be a whole number. But you can put it into your calculator, and whatever result you get, will be the answer. But it will be a negative solution, because some negative number, probably decimals, raised to the third power, will give you negative 15. So, again, the short answer of it is, yes, and here's a few illustrations to prove it. So, I'm Jimmy Chang, and that answers the question, can a cubed root be negative?


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