Here we will explain how to simplify the cube root of 12167 (∛12167). We start by labeling the parts of ∛12167 so it is easy to follow along:
∛12167 = 1∛12167 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 12167 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 12167, we first find the greatest perfect cube from the list of factors of 12167. The factors of 12167 are 1, 23, 529, and 12167.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 12167 (23 times 23 times 23 equals 12167).
To find the simplified radicand (r) in the cube root of 12167, we divide 12167 by 12167, which gives us 1.
To find the simplified coefficient of the radical (c) in the cube root of 12167, we take the cube root of 12167, which gives us 23.
That is how you simplify the cube root of 12167. Therefore, the cube root of 12167 in its simplest radical form is as follows:
∛12167 = 23
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