Here we will explain how to simplify the cube root of 13584 (∛13584). We start by labeling the parts of ∛13584 so it is easy to follow along:
∛13584 = 1∛13584 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 13584 in its simplest form means that you want the radicand to be as small as possible and the coefficient of the radical to be as large as possible.
To simplify the cube root of 13584, we first find the greatest perfect cube from the list of factors of 13584. The factors of 13584 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 283, 566, 849, 1132, 1698, 2264, 3396, 4528, 6792, and 13584.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 8 (2 times 2 times 2 equals 8).
To find the simplified radicand (r) in the cube root of 13584, we divide 13584 by 8, which gives us 1698.
To find the simplified coefficient of the radical (c) in the cube root of 13584, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 13584. Therefore, the cube root of 13584 in its simplest radical form is as follows:
∛13584 = 2∛1698
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