Here we will explain how to simplify the cube root of 75 (∛75). We start by labeling the parts of ∛75 so it is easy to follow along:
∛75 = 1∛75 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 75 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 75, we first find the greatest perfect cube from the list of factors of 75. The factors of 75 are 1, 3, 5, 15, 25, and 75.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 1 (1 times 1 times 1 equals 1).
To find the simplified radicand (r) in the cube root of 75, we divide 75 by 1, which gives us 75.
To find the simplified coefficient of the radical (c) in the cube root of 75, we take the cube root of 1, which gives us 1.
That is how you simplify the cube root of 75. Therefore, the cube root of 75 in its simplest radical form is as follows:
∛75 = ∛75
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