Here we will explain how to simplify the cube root of 5125 (∛5125). We start by labeling the parts of ∛5125 so it is easy to follow along:
∛5125 = 1∛5125 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 5125 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 5125, we first find the greatest perfect cube from the list of factors of 5125. The factors of 5125 are 1, 5, 25, 41, 125, 205, 1025, and 5125.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 125 (5 times 5 times 5 equals 125).
To find the simplified radicand (r) in the cube root of 5125, we divide 5125 by 125, which gives us 41.
To find the simplified coefficient of the radical (c) in the cube root of 5125, we take the cube root of 125, which gives us 5.
That is how you simplify the cube root of 5125. Therefore, the cube root of 5125 in its simplest radical form is as follows:
∛5125 = 5∛41
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