Here we will explain how to simplify the cube root of 1152 (∛1152). We start by labeling the parts of ∛1152 so it is easy to follow along:
∛1152 = 1∛1152 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 1152 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 1152, we first find the greatest perfect cube from the list of factors of 1152. The factors of 1152 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, and 1152.
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 1152, we divide 1152 by 64, which gives us 18.
To find the simplified coefficient of the radical (c) in the cube root of 1152, we take the cube root of 64, which gives us 4.
That is how you simplify the cube root of 1152. Therefore, the cube root of 1152 in its simplest radical form is as follows:
∛1152 = 4∛18
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