Here we will explain how to simplify the cube root of 456 (∛456). We start by labeling the parts of ∛456 so it is easy to follow along:
∛456 = 1∛456 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 456 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 456, we first find the greatest perfect cube from the list of factors of 456. The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, and 456.
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 456, we divide 456 by 8, which gives us 57.
To find the simplified coefficient of the radical (c) in the cube root of 456, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 456. Therefore, the cube root of 456 in its simplest radical form is as follows:
∛456 = 2∛57
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