Here we will explain how to simplify the cube root of 216 (∛216). We start by labeling the parts of ∛216 so it is easy to follow along:
∛216 = 1∛216 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 216 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 216, we first find the greatest perfect cube from the list of factors of 216. The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 216 (6 times 6 times 6 equals 216).
To find the simplified radicand (r) in the cube root of 216, we divide 216 by 216, which gives us 1.
To find the simplified coefficient of the radical (c) in the cube root of 216, we take the cube root of 216, which gives us 6.
That is how you simplify the cube root of 216. Therefore, the cube root of 216 in its simplest radical form is as follows:
∛216 = 6
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