Here we will explain how to simplify the cube root of 12312 (∛12312). We start by labeling the parts of ∛12312 so it is easy to follow along:
∛12312 = 1∛12312 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 12312 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 12312, we first find the greatest perfect cube from the list of factors of 12312. The factors of 12312 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 27, 36, 38, 54, 57, 72, 76, 81, 108, 114, 152, 162, 171, 216, 228, 324, 342, 456, 513, 648, 684, 1026, 1368, 1539, 2052, 3078, 4104, 6156, and 12312.
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 12312, we divide 12312 by 216, which gives us 57.
To find the simplified coefficient of the radical (c) in the cube root of 12312, we take the cube root of 216, which gives us 6.
That is how you simplify the cube root of 12312. Therefore, the cube root of 12312 in its simplest radical form is as follows:
∛12312 = 6∛57
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