Here we will explain how to simplify the cube root of 8512 (∛8512). We start by labeling the parts of ∛8512 so it is easy to follow along:
∛8512 = 1∛8512 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 8512 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 8512, we first find the greatest perfect cube from the list of factors of 8512. The factors of 8512 are 1, 2, 4, 7, 8, 14, 16, 19, 28, 32, 38, 56, 64, 76, 112, 133, 152, 224, 266, 304, 448, 532, 608, 1064, 1216, 2128, 4256, and 8512.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 64 (4 times 4 times 4 equals 64).
To find the simplified radicand (r) in the cube root of 8512, we divide 8512 by 64, which gives us 133.
To find the simplified coefficient of the radical (c) in the cube root of 8512, we take the cube root of 64, which gives us 4.
That is how you simplify the cube root of 8512. Therefore, the cube root of 8512 in its simplest radical form is as follows:
∛8512 = 4∛133
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