ʕ•ᴥ•ʔ Simplifying Cube Root Trick, with or without Negative Sign

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Whenever we see “roots”, let it be cubic roots or square roots, we know for sure that we will need to do prime factorization to find out the prime factors of the numbers. In this section, we use factors and multiples to find perfect cube whole numbers and cubic roots.

Welcome to this question here. This is very similar to the one before this, where you're trying to figure out what happens if it's a negative sign in the front or inside the radical, but this time the root number is a three which is an odd number, okay? So grab your calculator, if you punch in cube root of 27, you should get an answer that says three, okay, which is nice and easy. Now, if there is a negative sign in the front of the radical, you want to treat that negative one like that in the front of the radical, and you still go ahead and use your calculator or do your own work on a paper and figure out the cube root of 27, which is going to give you three, okay? So in the end you're just going to get a negative three, okay?

Coming down to the very last question right here, it's a cube root of negative 27. Now, if you remember, we don't square root any negative numbers because it will give a null solution, right? But this time you're not doing square root, you're doing cube root. So, if you're doing a cube root, the negative just comes out from the radical side and you still go ahead and figure out that the 27 separately from the negative side, okay? It's a little shortcut, so you still get a three.

So the answer is just a negative three. Now, does this only work or apply to cube roots only? No, it doesn't. As long as this number right here, is an odd number, okay? If it's an odd number you can always take out the negative from the radical, just put it on the outside and then just figure out the number and that's the answer, okay? Thanks for watching.

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