Here we will explain how to simplify the cube root of 14472 (∛14472). We start by labeling the parts of ∛14472 so it is easy to follow along:
∛14472 = 1∛14472 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 14472 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 14472, we first find the greatest perfect cube from the list of factors of 14472. The factors of 14472 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 67, 72, 108, 134, 201, 216, 268, 402, 536, 603, 804, 1206, 1608, 1809, 2412, 3618, 4824, 7236, and 14472.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 216 (6 times 6 times 6 equals 216).
To find the simplified radicand (r) in the cube root of 14472, we divide 14472 by 216, which gives us 67.
To find the simplified coefficient of the radical (c) in the cube root of 14472, we take the cube root of 216, which gives us 6.
That is how you simplify the cube root of 14472. Therefore, the cube root of 14472 in its simplest radical form is as follows:
∛14472 = 6∛67
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