Simplify Cube Root of 456

Here we will show you step-by-step how to simplify the cube root of 456. Before we continue, note that the cube root of 456 can be written as follows:

∛456

The ∛ symbol is called the radical sign. To simplify the cube root of 456 means to get the simplest radical form of ∛456.

Step 1: List Factors
We start by listing the factors of 456 like so:

1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, and 456

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 456 by the largest perfect cube to find the number that will go inside the radical.

456 / 8 = 57

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 456 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∛57

There you have it folks! Now you know how to simplify the cube root of 456. The answer to the cube root of 456 in its simplest radical form is displayed below:

∛456 = 2∛57

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Decimal Form
When we entered the cube root of 456 into our calculator, we got the answer to the cube root of 456 in decimal form:

∛456 ≈ 7.6970

Exponent Form
Here is how to write the cube root of 456 written with an exponent instead of a radical:

456^⅓ = 2 × 57^⅓

Simplify Cube Root of 457
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* List of Perfect Cubes