Simplify Cube Root of 7872

Here we will show you step-by-step how to simplify the cube root of 7872. Before we continue, note that the cube root of 7872 can be written as follows:

∛7872

The ∛ symbol is called the radical sign. To simplify the cube root of 7872 means to get the simplest radical form of ∛7872.

Step 1: List Factors
We start by listing the factors of 7872 like so:

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 41, 48, 64, 82, 96, 123, 164, 192, 246, 328, 492, 656, 984, 1312, 1968, 2624, 3936, and 7872

Step 2: Find Perfect Cubes
Next, we identify the perfect cubes* from the list of factors above:

1, 8, and 64

Step 3: Find the number to go inside the radical
From the list of perfect cubes, you see that 64 is the largest perfect cube. Now, divide 7872 by the largest perfect cube to find the number that will go inside the radical.

7872 / 64 = 123

Step 4: Find the number to go outside the radical
To find the number that will go outside the radical, we simply calculate the cube root of the largest perfect cube:

∛64 = 4

Step 5: Get the answer
Put Steps 3 and 4 together to get the cube root of 7872 in its simplest radical form. You put the result from Step 3 inside the radical and the result from Step 4 outside the radical:

4∛123

There you have it folks! Now you know how to simplify the cube root of 7872. The answer to the cube root of 7872 in its simplest radical form is displayed below:

∛7872 = 4∛123

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Decimal Form
When we entered the cube root of 7872 into our calculator, we got the answer to the cube root of 7872 in decimal form:

∛7872 ≈ 19.8928

Exponent Form
Here is how to write the cube root of 7872 written with an exponent instead of a radical:

7872^⅓ = 4 × 123^⅓

Simplify Cube Root of 7873
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* List of Perfect Cubes