Simplify Cube Root of 8192

Here we will show you step-by-step how to simplify the cube root of 8192. Before we continue, note that the cube root of 8192 can be written as follows:

∛8192

The ∛ symbol is called the radical sign. To simplify the cube root of 8192 means to get the simplest radical form of ∛8192.

Step 1: List Factors
We start by listing the factors of 8192 like so:

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, and 8192

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

1, 8, 64, 512, and 4096

Step 3: Find the number to go inside the radical
From the list of perfect cubes, you see that 4096 is the largest perfect cube. Now, divide 8192 by the largest perfect cube to find the number that will go inside the radical.

8192 / 4096 = 2

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:

∛4096 = 16

Step 5: Get the answer
Put Steps 3 and 4 together to get the cube root of 8192 in its simplest radical form. You put the result from Step 3 inside the radical and the result from Step 4 outside the radical:

16∛2

There you have it folks! Now you know how to simplify the cube root of 8192. The answer to the cube root of 8192 in its simplest radical form is displayed below:

∛8192 = 16∛2

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Decimal Form
When we entered the cube root of 8192 into our calculator, we got the answer to the cube root of 8192 in decimal form:

∛8192 ≈ 20.1587

Exponent Form
Here is how to write the cube root of 8192 written with an exponent instead of a radical:

8192^⅓ = 16 × 2^⅓

Simplify Cube Root of 8193
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* List of Perfect Cubes