Here we will explain how to simplify the cube root of 83640 (∛83640). We start by labeling the parts of ∛83640 so it is easy to follow along:
∛83640 = 1∛83640 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 83640 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 83640, we first find the greatest perfect cube from the list of factors of 83640. The factors of 83640 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 41, 51, 60, 68, 82, 85, 102, 120, 123, 136, 164, 170, 204, 205, 246, 255, 328, 340, 408, 410, 492, 510, 615, 680, 697, 820, 984, 1020, 1230, 1394, 1640, 2040, 2091, 2460, 2788, 3485, 4182, 4920, 5576, 6970, 8364, 10455, 13940, 16728, 20910, 27880, 41820, and 83640.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 8 (2 times 2 times 2 equals 8).
To find the simplified radicand (r) in the cube root of 83640, we divide 83640 by 8, which gives us 10455.
To find the simplified coefficient of the radical (c) in the cube root of 83640, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 83640. Therefore, the cube root of 83640 in its simplest radical form is as follows:
∛83640 = 2∛10455
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