Here we will explain how to simplify the cube root of 38416 (∛38416). We start by labeling the parts of ∛38416 so it is easy to follow along:
∛38416 = 1∛38416 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 38416 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 38416, we first find the greatest perfect cube from the list of factors of 38416. The factors of 38416 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 343, 392, 686, 784, 1372, 2401, 2744, 4802, 5488, 9604, 19208, and 38416.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 2744 (14 times 14 times 14 equals 2744).
To find the simplified radicand (r) in the cube root of 38416, we divide 38416 by 2744, which gives us 14.
To find the simplified coefficient of the radical (c) in the cube root of 38416, we take the cube root of 2744, which gives us 14.
That is how you simplify the cube root of 38416. Therefore, the cube root of 38416 in its simplest radical form is as follows:
∛38416 = 14∛14
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