Here we will explain how to simplify the cube root of 87552 (∛87552). We start by labeling the parts of ∛87552 so it is easy to follow along:
∛87552 = 1∛87552 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 87552 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 87552, we first find the greatest perfect cube from the list of factors of 87552. The factors of 87552 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 32, 36, 38, 48, 57, 64, 72, 76, 96, 114, 128, 144, 152, 171, 192, 228, 256, 288, 304, 342, 384, 456, 512, 576, 608, 684, 768, 912, 1152, 1216, 1368, 1536, 1824, 2304, 2432, 2736, 3648, 4608, 4864, 5472, 7296, 9728, 10944, 14592, 21888, 29184, 43776, and 87552.
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 87552, we divide 87552 by 512, which gives us 171.
To find the simplified coefficient of the radical (c) in the cube root of 87552, we take the cube root of 512, which gives us 8.
That is how you simplify the cube root of 87552. Therefore, the cube root of 87552 in its simplest radical form is as follows:
∛87552 = 8∛171
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