Here we will explain how to simplify the cube root of 8625 (∛8625). We start by labeling the parts of ∛8625 so it is easy to follow along:
∛8625 = 1∛8625 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 8625 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 8625, we first find the greatest perfect cube from the list of factors of 8625. The factors of 8625 are 1, 3, 5, 15, 23, 25, 69, 75, 115, 125, 345, 375, 575, 1725, 2875, and 8625.
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 8625, we divide 8625 by 125, which gives us 69.
To find the simplified coefficient of the radical (c) in the cube root of 8625, we take the cube root of 125, which gives us 5.
That is how you simplify the cube root of 8625. Therefore, the cube root of 8625 in its simplest radical form is as follows:
∛8625 = 5∛69
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