Here we will explain how to simplify the cube root of 16608 (∛16608). We start by labeling the parts of ∛16608 so it is easy to follow along:
∛16608 = 1∛16608 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 16608 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 16608, we first find the greatest perfect cube from the list of factors of 16608. The factors of 16608 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 173, 346, 519, 692, 1038, 1384, 2076, 2768, 4152, 5536, 8304, and 16608.
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 16608, we divide 16608 by 8, which gives us 2076.
To find the simplified coefficient of the radical (c) in the cube root of 16608, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 16608. Therefore, the cube root of 16608 in its simplest radical form is as follows:
∛16608 = 2∛2076
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