Here we will explain how to simplify the cube root of 4096 (∛4096). We start by labeling the parts of ∛4096 so it is easy to follow along:
∛4096 = 1∛4096 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 4096 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 4096, we first find the greatest perfect cube from the list of factors of 4096. The factors of 4096 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, and 4096.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 4096 (16 times 16 times 16 equals 4096).
To find the simplified radicand (r) in the cube root of 4096, we divide 4096 by 4096, which gives us 1.
To find the simplified coefficient of the radical (c) in the cube root of 4096, we take the cube root of 4096, which gives us 16.
That is how you simplify the cube root of 4096. Therefore, the cube root of 4096 in its simplest radical form is as follows:
∛4096 = 16
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