Here we will explain how to simplify the cube root of 14800 (∛14800). We start by labeling the parts of ∛14800 so it is easy to follow along:
∛14800 = 1∛14800 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 14800 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 14800, we first find the greatest perfect cube from the list of factors of 14800. The factors of 14800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 37, 40, 50, 74, 80, 100, 148, 185, 200, 296, 370, 400, 592, 740, 925, 1480, 1850, 2960, 3700, 7400, and 14800.
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 14800, we divide 14800 by 8, which gives us 1850.
To find the simplified coefficient of the radical (c) in the cube root of 14800, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 14800. Therefore, the cube root of 14800 in its simplest radical form is as follows:
∛14800 = 2∛1850
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