Here we will explain how to simplify the cube root of 8064 (∛8064). We start by labeling the parts of ∛8064 so it is easy to follow along:
∛8064 = 1∛8064 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 8064 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 8064, we first find the greatest perfect cube from the list of factors of 8064. The factors of 8064 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 288, 336, 384, 448, 504, 576, 672, 896, 1008, 1152, 1344, 2016, 2688, 4032, and 8064.
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 8064, we divide 8064 by 64, which gives us 126.
To find the simplified coefficient of the radical (c) in the cube root of 8064, we take the cube root of 64, which gives us 4.
That is how you simplify the cube root of 8064. Therefore, the cube root of 8064 in its simplest radical form is as follows:
∛8064 = 4∛126
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