Simplify Cube Root of 3680

Here we will show you step-by-step how to simplify the cube root of 3680. Before we continue, note that the cube root of 3680 can be written as follows:

∛3680

The ∛ symbol is called the radical sign. To simplify the cube root of 3680 means to get the simplest radical form of ∛3680.

Step 1: List Factors
We start by listing the factors of 3680 like so:

1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 80, 92, 115, 160, 184, 230, 368, 460, 736, 920, 1840, and 3680

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

1 and 8

Step 3: Find the number to go inside the radical
From the list of perfect cubes, you see that 8 is the largest perfect cube. Now, divide 3680 by the largest perfect cube to find the number that will go inside the radical.

3680 / 8 = 460

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:

∛8 = 2

Step 5: Get the answer
Put Steps 3 and 4 together to get the cube root of 3680 in its simplest radical form. You put the result from Step 3 inside the radical and the result from Step 4 outside the radical:

2∛460

There you have it folks! Now you know how to simplify the cube root of 3680. The answer to the cube root of 3680 in its simplest radical form is displayed below:

∛3680 = 2∛460

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Decimal Form
When we entered the cube root of 3680 into our calculator, we got the answer to the cube root of 3680 in decimal form:

∛3680 ≈ 15.4389

Exponent Form
Here is how to write the cube root of 3680 written with an exponent instead of a radical:

3680^⅓ = 2 × 460^⅓

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* List of Perfect Cubes