Here we will explain how to simplify the cube root of 2401 (∛2401). We start by labeling the parts of ∛2401 so it is easy to follow along:
∛2401 = 1∛2401 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 2401 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 2401, we first find the greatest perfect cube from the list of factors of 2401. The factors of 2401 are 1, 7, 49, 343, and 2401.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 343 (7 times 7 times 7 equals 343).
To find the simplified radicand (r) in the cube root of 2401, we divide 2401 by 343, which gives us 7.
To find the simplified coefficient of the radical (c) in the cube root of 2401, we take the cube root of 343, which gives us 7.
That is how you simplify the cube root of 2401. Therefore, the cube root of 2401 in its simplest radical form is as follows:
∛2401 = 7∛7
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