Simplify Cube Root of 72

Here we will show you step-by-step how to simplify the cube root of 72. Before we continue, note that the cube root of 72 can be written as follows:

∛72

The ∛ symbol is called the radical sign. To simplify the cube root of 72 means to get the simplest radical form of ∛72.

Step 1: List Factors
We start by listing the factors of 72 like so:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72

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

72 / 8 = 9

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 72 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∛9

There you have it folks! Now you know how to simplify the cube root of 72. The answer to the cube root of 72 in its simplest radical form is displayed below:

∛72 = 2∛9

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Decimal Form
When we entered the cube root of 72 into our calculator, we got the answer to the cube root of 72 in decimal form:

∛72 ≈ 4.1602

Exponent Form
Here is how to write the cube root of 72 written with an exponent instead of a radical:

72^⅓ = 2 × 9^⅓

Simplify Cube Root of 73
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* List of Perfect Cubes