Here we will explain how to simplify the cube root of 5184 (∛5184). We start by labeling the parts of ∛5184 so it is easy to follow along:
∛5184 = 1∛5184 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 5184 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 5184, we first find the greatest perfect cube from the list of factors of 5184. The factors of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, and 5184.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 1728 (12 times 12 times 12 equals 1728).
To find the simplified radicand (r) in the cube root of 5184, we divide 5184 by 1728, which gives us 3.
To find the simplified coefficient of the radical (c) in the cube root of 5184, we take the cube root of 1728, which gives us 12.
That is how you simplify the cube root of 5184. Therefore, the cube root of 5184 in its simplest radical form is as follows:
∛5184 = 12∛3
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