Here we will explain how to simplify the cube root of 1408 (∛1408). We start by labeling the parts of ∛1408 so it is easy to follow along:
∛1408 = 1∛1408 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 1408 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 1408, we first find the greatest perfect cube from the list of factors of 1408. The factors of 1408 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 352, 704, and 1408.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 64 (4 times 4 times 4 equals 64).
To find the simplified radicand (r) in the cube root of 1408, we divide 1408 by 64, which gives us 22.
To find the simplified coefficient of the radical (c) in the cube root of 1408, we take the cube root of 64, which gives us 4.
That is how you simplify the cube root of 1408. Therefore, the cube root of 1408 in its simplest radical form is as follows:
∛1408 = 4∛22
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