Here we will explain how to simplify the cube root of 34416 (∛34416). We start by labeling the parts of ∛34416 so it is easy to follow along:
∛34416 = 1∛34416 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 34416 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 34416, we first find the greatest perfect cube from the list of factors of 34416. The factors of 34416 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 239, 478, 717, 956, 1434, 1912, 2151, 2868, 3824, 4302, 5736, 8604, 11472, 17208, and 34416.
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 34416, we divide 34416 by 8, which gives us 4302.
To find the simplified coefficient of the radical (c) in the cube root of 34416, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 34416. Therefore, the cube root of 34416 in its simplest radical form is as follows:
∛34416 = 2∛4302
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