Here we will explain how to simplify the cube root of 75712 (∛75712). We start by labeling the parts of ∛75712 so it is easy to follow along:
∛75712 = 1∛75712 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 75712 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 75712, we first find the greatest perfect cube from the list of factors of 75712. The factors of 75712 are 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 64, 91, 104, 112, 169, 182, 208, 224, 338, 364, 416, 448, 676, 728, 832, 1183, 1352, 1456, 2366, 2704, 2912, 4732, 5408, 5824, 9464, 10816, 18928, 37856, and 75712.
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 75712, we divide 75712 by 64, which gives us 1183.
To find the simplified coefficient of the radical (c) in the cube root of 75712, we take the cube root of 64, which gives us 4.
That is how you simplify the cube root of 75712. Therefore, the cube root of 75712 in its simplest radical form is as follows:
∛75712 = 4∛1183
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