Here we will explain how to simplify the cube root of 14400 (∛14400). We start by labeling the parts of ∛14400 so it is easy to follow along:
∛14400 = 1∛14400 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 14400 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 14400, we first find the greatest perfect cube from the list of factors of 14400. The factors of 14400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 144, 150, 160, 180, 192, 200, 225, 240, 288, 300, 320, 360, 400, 450, 480, 576, 600, 720, 800, 900, 960, 1200, 1440, 1600, 1800, 2400, 2880, 3600, 4800, 7200, and 14400.
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 14400, we divide 14400 by 64, which gives us 225.
To find the simplified coefficient of the radical (c) in the cube root of 14400, we take the cube root of 64, which gives us 4.
That is how you simplify the cube root of 14400. Therefore, the cube root of 14400 in its simplest radical form is as follows:
∛14400 = 4∛225
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