Cube Root: Definition, Formula & Examples

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  • 0:05 Definition of a Cube Root
  • 0:16 Moving Cubes
  • 1:25 Perfect Cubes and…
  • 2:17 Calculator Connection
  • 3:08 Lesson Summary
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Lesson Transcript
Instructor: Jennie Brady

Jennie has eight years experience teaching high school math and has a Master's degree in Education Leadership.

In this lesson, we're going to discover the world of cube roots! By the time we're done, you should be able to define what a cube root is, explain how to solve for the cube root of a number, and be familiar with several common cube roots.

Definition of a Cube Root

First things first. A cube root is the number that multiplies by itself three times in order to create a cubic value. That was a bit of a mouthful. Let's break this down with an example.

Moving Cubes

I'm getting ready to move across town, so I am collecting as many boxes as I can to get packed up. I had a friend offer me some boxes, but she mentioned that each side is only 2 feet long, wide, and high, and they may not hold very much.

Well, I can use math to figure out the volume of each box so I know how much of my stuff they will hold. Remember, the formula to find the volume of a rectangular prism is length * width * height. Since each side of the box measures 2 feet, I would perform the following calculation:

Volume of Each Box
2 * 2 * 2
4 * 2

This means that each box has 8 cubic feet of space. That's a good size box! Hey, did you notice that the boxes are in the shape of cubes? That's why we say that you have 'cubed' a number when you multiply it by itself three times. I multiplied 2 by itself three times, or cubed it, to get 8.

Now we can work backwards and apply the cube root function to the number 8, resulting in 2. This means that the cube root of 8 is 2!

Perfect Cubes and the Cube Roots

Now that we have a better understanding of the definition of cube roots, let's look at some perfect cubes. A perfect cube is an integer that has an integer value as the cube root. Remember that an integer is a value that corresponds to the ticks on the number line. This means that an integer does not have any fractions or decimals with it. Using the numbers from above, both 8 and 2 are integers, so that means 8 is a perfect cube.

Perfect Cube Cube Root
8 2
27 3
64 4
125 5
216 6

If it seems like I'm pulling numbers from a hat, let me show you the work:

Cube Root Working... Working... Perfect Cube
2 2 * 2 * 2 4 * 2 8
3 3 * 3 * 3 9 * 3 27
4 4 * 4 * 4 16 * 4 64
5 5 * 5 * 5 25 * 5 125
6 6 * 6 * 6 36 * 6 216

Now here's a neat connection: Did you notice the perfect squares in the second set of work for each of the examples? That means that finding the cube of a number is the same as multiplying the number by its square. I realize that I'm a special kind of math nerd, but I think that's pretty cool!

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