Here we will explain how to simplify the cube root of 14688 (∛14688). We start by labeling the parts of ∛14688 so it is easy to follow along:
∛14688 = 1∛14688 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 14688 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 14688, we first find the greatest perfect cube from the list of factors of 14688. The factors of 14688 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 32, 34, 36, 48, 51, 54, 68, 72, 96, 102, 108, 136, 144, 153, 204, 216, 272, 288, 306, 408, 432, 459, 544, 612, 816, 864, 918, 1224, 1632, 1836, 2448, 3672, 4896, 7344, and 14688.
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 14688, we divide 14688 by 216, which gives us 68.
To find the simplified coefficient of the radical (c) in the cube root of 14688, we take the cube root of 216, which gives us 6.
That is how you simplify the cube root of 14688. Therefore, the cube root of 14688 in its simplest radical form is as follows:
∛14688 = 6∛68
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