Here we will explain how to simplify the cube root of 16875 (∛16875). We start by labeling the parts of ∛16875 so it is easy to follow along:
∛16875 = 1∛16875 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 16875 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 16875, we first find the greatest perfect cube from the list of factors of 16875. The factors of 16875 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 125, 135, 225, 375, 625, 675, 1125, 1875, 3375, 5625, and 16875.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 3375 (15 times 15 times 15 equals 3375).
To find the simplified radicand (r) in the cube root of 16875, we divide 16875 by 3375, which gives us 5.
To find the simplified coefficient of the radical (c) in the cube root of 16875, we take the cube root of 3375, which gives us 15.
That is how you simplify the cube root of 16875. Therefore, the cube root of 16875 in its simplest radical form is as follows:
∛16875 = 15∛5
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