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How to Find Cube Roots and Perfect Cubes

how to find cube root: Smiling girl doing her homework

In order to figure out how to find cube roots, you must review square roots. Finding the square root of a number means determining what other number needs to be multiplied by itself to get the original number. For example:

√81 = 9

What Are Cube Roots?

Finding cube roots takes it a step further. Below is an example of a number being cubed:

4³ = 64

4 x 4 x 4 = 64

The process of cubing is multiplying a number by itself three times, as indicated by the exponent of 3. Let's take the example of 64 again. To find its cube root, you need to know that 4 needs to be multiplied by itself three times to get the final result of 64.

If you want to calculate cube roots, you must list a small 3 outside the root symbol:

³√8 = 2

Finding the Cube Root of Negative Numbers

Unlike square roots, you can take the cube root of a negative number. This is because a negative number multiplied by itself 3 times will always equal a negative. Because of this, the result of cubing a number doesn't have to be a whole number, it can be a negative or positive number:

³√-216 = 6

What Is a Perfect Cube?

Now that we've seen how to find the cube root of a number, let's take a look at perfect cubes. When using a cube root calculator, you can technically take the cube root of any number. However, you will sometimes end up with an answer that has tons of decimals. But this doesn't happen when you take the cube root of a perfect cube.

A perfect cube is the integer that you get when you raise another integer to the third power. A perfect cube integer cannot be a decimal or fraction. The same goes for the number that is being raised to the third power.

Here is a list of perfect cubes:

1³ = 1

2³ = 4

3³ = 27

4³ = 64

5³ = 125

6³ = 216

7³ = 343

Keep this list handy for when you don't have a cube root calculator.

How to Find Cube Roots

Finding cube roots is simply applying what you've learned about square roots and taking it a step further. So instead of multiplying a number by itself twice, cubing is the process of multiplying a number by itself three times. Similarly, perfect cubes are just like perfect squares but with the third root taken instead of the second.

When you know how to cube a number, how to take the cubed root of a positive and negative number, and are familiar with perfect cubes, you'll be ready to master more complex math concepts that involve cubed roots.

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