Here we will explain how to simplify the cube root of 12384 (∛12384). We start by labeling the parts of ∛12384 so it is easy to follow along:
∛12384 = 1∛12384 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 12384 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 12384, we first find the greatest perfect cube from the list of factors of 12384. The factors of 12384 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 43, 48, 72, 86, 96, 129, 144, 172, 258, 288, 344, 387, 516, 688, 774, 1032, 1376, 1548, 2064, 3096, 4128, 6192, and 12384.
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 12384, we divide 12384 by 8, which gives us 1548.
To find the simplified coefficient of the radical (c) in the cube root of 12384, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 12384. Therefore, the cube root of 12384 in its simplest radical form is as follows:
∛12384 = 2∛1548
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