Here we will explain how to simplify the cube root of 1208 (∛1208). We start by labeling the parts of ∛1208 so it is easy to follow along:
∛1208 = 1∛1208 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 1208 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 1208, we first find the greatest perfect cube from the list of factors of 1208. The factors of 1208 are 1, 2, 4, 8, 151, 302, 604, and 1208.
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 1208, we divide 1208 by 8, which gives us 151.
To find the simplified coefficient of the radical (c) in the cube root of 1208, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 1208. Therefore, the cube root of 1208 in its simplest radical form is as follows:
∛1208 = 2∛151
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