Here we will explain how to simplify the cube root of 13824 (∛13824). We start by labeling the parts of ∛13824 so it is easy to follow along:
∛13824 = 1∛13824 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 13824 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 13824, we first find the greatest perfect cube from the list of factors of 13824. The factors of 13824 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1152, 1536, 1728, 2304, 3456, 4608, 6912, and 13824.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 13824 (24 times 24 times 24 equals 13824).
To find the simplified radicand (r) in the cube root of 13824, we divide 13824 by 13824, which gives us 1.
To find the simplified coefficient of the radical (c) in the cube root of 13824, we take the cube root of 13824, which gives us 24.
That is how you simplify the cube root of 13824. Therefore, the cube root of 13824 in its simplest radical form is as follows:
∛13824 = 24
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