Here we will explain how to simplify the cube root of 13776 (∛13776). We start by labeling the parts of ∛13776 so it is easy to follow along:
∛13776 = 1∛13776 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 13776 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 13776, we first find the greatest perfect cube from the list of factors of 13776. The factors of 13776 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 41, 42, 48, 56, 82, 84, 112, 123, 164, 168, 246, 287, 328, 336, 492, 574, 656, 861, 984, 1148, 1722, 1968, 2296, 3444, 4592, 6888, and 13776.
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 13776, we divide 13776 by 8, which gives us 1722.
To find the simplified coefficient of the radical (c) in the cube root of 13776, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 13776. Therefore, the cube root of 13776 in its simplest radical form is as follows:
∛13776 = 2∛1722
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