Here we will explain how to simplify the cube root of 82752 (∛82752). We start by labeling the parts of ∛82752 so it is easy to follow along:
∛82752 = 1∛82752 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 82752 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 82752, we first find the greatest perfect cube from the list of factors of 82752. The factors of 82752 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 431, 862, 1293, 1724, 2586, 3448, 5172, 6896, 10344, 13792, 20688, 27584, 41376, and 82752.
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 82752, we divide 82752 by 64, which gives us 1293.
To find the simplified coefficient of the radical (c) in the cube root of 82752, we take the cube root of 64, which gives us 4.
That is how you simplify the cube root of 82752. Therefore, the cube root of 82752 in its simplest radical form is as follows:
∛82752 = 4∛1293
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