Here we will explain how to simplify the cube root of 24375 (∛24375). We start by labeling the parts of ∛24375 so it is easy to follow along:
∛24375 = 1∛24375 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 24375 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 24375, we first find the greatest perfect cube from the list of factors of 24375. The factors of 24375 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 125, 195, 325, 375, 625, 975, 1625, 1875, 4875, 8125, and 24375.
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 24375, we divide 24375 by 125, which gives us 195.
To find the simplified coefficient of the radical (c) in the cube root of 24375, we take the cube root of 125, which gives us 5.
That is how you simplify the cube root of 24375. Therefore, the cube root of 24375 in its simplest radical form is as follows:
∛24375 = 5∛195
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