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How to Find the Cube Root of a Number

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  • 0:05 What is a Cube Root?
  • 1:08 Perfect Cubes
  • 2:32 Finding a Cube Root
  • 4:21 Negative Cube Roots
  • 4:45 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will understand the process of finding the cube root of a number. Learn which numbers have an easy cube root to find and what the cube root means.

What is a Cube Root?

In this video lesson, we will look at cube roots and how to find them. To begin, did you know that a cube root actually has a lot to do with cubes? In math, we define a cube root as the special value that when multiplied three times gives you your desired number. For example, the cube root of 27 is 3 because 3 * 3 * 3 (3 multiplied three times or cubed) gets you 27.

What does this have to do with cubes? Well, if we were to visualize the multiplication problem of 3 * 3 * 3, we would see a cube that is three blocks wide, three blocks long, and three blocks high. It is a cube because all three sides are the same length. All the sides have three blocks each. Every cube root will be like that.

In math, we have a special symbol for the cube root. We use the same symbol as we do for the square root, but this time, we will have a little 3 in the dip of the square root symbol. It looks like this:

cube root

Perfect Cubes

The example that we just saw also happens to be an example of a perfect cube. A perfect cube is a cube of a whole number. 27 is a perfect cube because to get 27, we need to cube the 3. Think back to the cube. It's a perfect cube because all the building blocks are whole pieces. To find a perfect cube, we take any whole number and cube it, meaning we multiply it by itself three times. Knowing our perfect cubes helps us to find cube roots easily. If we started with the 1 and found perfect cubes for our numbers up to 10, we would get this list:

1 2 3 4 5 6 7 8 9 10
Perfect Cube: 1 8 27 64 125 216 343 512 729 1000

Perfect cube of 1 is 1. Perfect cube of 2 is 8. Perfect cube of 3 is 27. Perfect cube of 4 is 64. Perfect cube of 5 is 125. Perfect cube of 6 is 216. Perfect cube of 7 is 343. Perfect cube of 8 is 512. Perfect cube of 9 is 729. Perfect cube of 10 is 1000.

We can build onto our list by cubing the rest of the numbers. For example, to find the perfect cube of 11, we can cube 11, multiplying it three times: 11 * 11 * 11 = 1331.

Finding a Cube Root

Now, how can we use our perfect cube information to help us find our cube roots? If we are asked to find the cube root of 64, we can refer to our list, find 64, and see that the cube root of 64 is 4 because to get 64 we can multiply the 4 three times, cubing it. If the number we are taking the cube root of is a perfect cube, our answer will be in our list of perfect cubes.

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