Here we will explain how to simplify the cube root of 424 (∛424). We start by labeling the parts of ∛424 so it is easy to follow along:
∛424 = 1∛424 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 424 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 424, we first find the greatest perfect cube from the list of factors of 424. The factors of 424 are 1, 2, 4, 8, 53, 106, 212, and 424.
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 424, we divide 424 by 8, which gives us 53.
To find the simplified coefficient of the radical (c) in the cube root of 424, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 424. Therefore, the cube root of 424 in its simplest radical form is as follows:
∛424 = 2∛53
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