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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.

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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.

We can also use our list to help us find the cube roots of numbers that are not perfect cubes. For example, if we are asked to find the cube root of 5, we can look at our list and see that 5 is between 1 and 8, the first two perfect cubes. This tells us that our answer must lie between 1 and 2.

To actually find our answer, we will have to guess and do trial and error.We can try 1.5 and cube it to see if we get 5 for our answer: 1.5 * 1.5 * 1.5 = 3.

375. We are under 5, so we can try 1.8 next: 1.8 * 1.8 * 1.8 = 5.832.

We are over this time, so that means we need to lower our guess. Let’s try 1.75: 1.75 * 1.75 * 1.

75 = 5.359375. We are getting closer and closer. As you can see, we will need to keep repeating this process for a bit. Using our calculator and taking the cube root of 5, we see that we get an answer of 1.7099759. .

. We got a decimal that seems to go on and on. Without using a calculator, we can only approximate our cube root, at best. But our list of perfect cubes does give us an approximate idea of our answer.

Negative Cube Roots

We can also take our list of perfect cubes and expand it to negative numbers. That’s right; unlike square roots, we can have negative cube roots. For example, -2 * -2 * -2 = -8. So, the cube root of -8 is -2. Try this on your calculator, and you will see that you won’t get an error but your answer of -2.

Lesson Summary

Let’s review what we’ve learned. A cube root is a special value that when multiplied three times gives you your desired number.

A perfect cube is a cube of a whole number. To find the cube root of a perfect cube, we can use a list of perfect cubes to find our answer. We can use our list of perfect cubes to approximate our answer for the cube roots of other numbers. The key thing to remember is that the answer to a cube root is a value that when multiplied three times, gives you your desired number.

Learning Outcomes

Once you have finished this lesson, you should be able to:

  • Explain what a cube root is
  • Identify a perfect cube
  • Calculate a cube root

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