Here we will explain how to simplify the cube root of 31232 (∛31232). We start by labeling the parts of ∛31232 so it is easy to follow along:
∛31232 = 1∛31232 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 31232 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 31232, we first find the greatest perfect cube from the list of factors of 31232. The factors of 31232 are 1, 2, 4, 8, 16, 32, 61, 64, 122, 128, 244, 256, 488, 512, 976, 1952, 3904, 7808, 15616, and 31232.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 512 (8 times 8 times 8 equals 512).
To find the simplified radicand (r) in the cube root of 31232, we divide 31232 by 512, which gives us 61.
To find the simplified coefficient of the radical (c) in the cube root of 31232, we take the cube root of 512, which gives us 8.
That is how you simplify the cube root of 31232. Therefore, the cube root of 31232 in its simplest radical form is as follows:
∛31232 = 8∛61
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