What is the perfect cube of 6912?

Here we will show you how to get the factors of cube root of 6912 (factors of ∛6912). We define factors of cube root of 6912 as any integer (whole number) or cube root that you can evenly divide into cube root of 6912. Furthermore, if you divide ∛6912 by a factor of ∛6912, it will result in another factor of ∛6912.

First, we will find all the cube roots that we can evenly divide into cube root of 6912. We do this by finding all the factors of 6912 and add a radical (∛) to them like this:

∛1, ∛2, ∛3, ∛4, ∛6, ∛8, ∛9, ∛12, ∛16, ∛18, ∛24, ∛27, ∛32, ∛36, ∛48, ∛54, ∛64, ∛72, ∛96, ∛108, ∛128, ∛144, ∛192, ∛216, ∛256, ∛288, ∛384, ∛432, ∛576, ∛768, ∛864, ∛1152, ∛1728, ∛2304, ∛3456, and ∛6912

Next, we will find all the integers that we can evenly divide into cube root of 6912. We do that by first identifying the perfect cube roots from the list above:

∛1, ∛8, ∛27, ∛64, ∛216, and ∛1728

Then, we take the cube root of the perfect cube roots to get the integers that we can evenly divide into cube root of 6912.

1, 2, 3, 4, 6, and 12

Factors of cube root of 6912 are the two lists above combined. Thus, factors of cube root of 6912 (cube roots and integers) are as follows:

1, 2, 3, 4, 6, 12, ∛1, ∛2, ∛3, ∛4, ∛6, ∛8, ∛9, ∛12, ∛16, ∛18, ∛24, ∛27, ∛32, ∛36, ∛48, ∛54, ∛64, ∛72, ∛96, ∛108, ∛128, ∛144, ∛192, ∛216, ∛256, ∛288, ∛384, ∛432, ∛576, ∛768, ∛864, ∛1152, ∛1728, ∛2304, ∛3456, and ∛6912

Like we said above, cube root of 6912 divided by any of its factors, will result in another of its factors. Therefore, if you divide ∛6912 by any of factors above, you will see that it results in one of the other factors.

What can you do with this information? For one, you can get cube root of 6912 in its simplest form. Cube root of 6912 simplified is the largest integer factor times the cube root of 6912 divided by the largest perfect cube root. Thus, here is the math to get cube root of 6912 in its simplest radical form:

What is a cube root?

In arithmetic and algebra, the cube of a number n is its third power: the result of the number multiplied by itself twice: n³ = n * n * n. It is also the number multiplied by its square: n³ = n * n².
This is also the volume formula for a geometric cube with sides of length n, giving rise to the name. The inverse operation of finding a number whose cube is n is called extracting the cube root of n. It determines the side of the cube of a given volume. It is also n raised to the one-third power.
Both cube and cube root are odd functions: (-n)³ = -(n³). The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2³ = 8 or (x + 1)³.

In math, the cube root of a number like 6912 is a number that, when multiplied by itself two times, is equal to 6912.

We would show this in mathematical form with the cube root symbol, which is similar to the radical symbol (√) used in a square root, but which also has the number 3 above the symbol (this number is called the index):

∛6912

So, the √ is called the radical symbol, the little 3 above it is the index (which means multiply by itself two more times), and the number, 6912, is called the radicand.

To explain the cube root a little more, the cube root of the number 6912 is a number (which we call n) that when multiplied by itself twice is equal to 6912:

n × n × n = 6912

∛6912 is the same as 6912⅓ and so if you are solving a problem in a spreadsheet like Excel, Numbers, or Google Sheets, you can use =6912^(1/3) to calculate the cube root.

For the purposes of this article, we'll use a scientific calculator to work out the cubic root by typing the number 6912 and pressing the [∛x] button, to give the following answer:

∛6912 ≈ 19.048812623618

Is 6912 a Perfect Cube?

When the cube root of a given number is a whole number, this is called a perfect cube. Perfect cubes are important for many mathematical functions and are used in everything from carpentry through to more advanced topics like physics and astronomy.

If we look at the number 6912, we know that the cube root is 19.048812623618, and since this is not a whole number, we also know that 6912 is not a perfect cube.

If you want to learn more about perfect cube numbers we have a list of perfect cubes which covers the first 500 perfect cube numbers.

Is the Cube Root of 6912 a Rational or Irrational Number?

Another common question you might find when working with the roots of a number like 6912 is whether the given number is rational or irrational. Rational numbers can be written as a fraction and irrational numbers can't.

The quickest way to check if a number is rational or irrational is to determine if it is a perfect cube. If it is, then it's a rational number, but if it is not a perfect cube then it is an irrational number.

We already know that 6912 is not a rational number then, because we know it is not a perfect cube.

Rounding the Cube Root of 6912

Sometimes when you work with the cube root of 6912 you might need to round the answer down to a specific number of decimal places:

10th: ∛6912 = 19.0

100th: ∛6912 = 19.05

1000th: ∛6912 = 19.049

Simplifying the Cube Root of 6912

It is possible to simplify the cube root of 6912 if the radicand can be made smaller. When that is possible, it is called the cube root of 6912 in its simplest radical form.

In this example, the cube root of 6912 in its simplest form is:

∛6912 = 12∛1

Practice Cube Roots Using Examples

If you want to continue learning about cubic roots, take a look at the random calculations in the sidebar to the right of this blog post.

We have listed a selection of completely random numbers that you can click through and follow the information on calculating the cubic root of that number to help you understand number roots.

Calculate Cube Square Root Problem

Enter your number in box A below and click "Calculate" to work out the cube root of the given number.

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