Here we will explain how to simplify the cube root of 54880 (∛54880). We start by labeling the parts of ∛54880 so it is easy to follow along:
∛54880 = 1∛54880 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 54880 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 54880, we first find the greatest perfect cube from the list of factors of 54880. The factors of 54880 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 49, 56, 70, 80, 98, 112, 140, 160, 196, 224, 245, 280, 343, 392, 490, 560, 686, 784, 980, 1120, 1372, 1568, 1715, 1960, 2744, 3430, 3920, 5488, 6860, 7840, 10976, 13720, 27440, and 54880.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 2744 (14 times 14 times 14 equals 2744).
To find the simplified radicand (r) in the cube root of 54880, we divide 54880 by 2744, which gives us 20.
To find the simplified coefficient of the radical (c) in the cube root of 54880, we take the cube root of 2744, which gives us 14.
That is how you simplify the cube root of 54880. Therefore, the cube root of 54880 in its simplest radical form is as follows:
∛54880 = 14∛20
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