Here we will explain how to simplify the cube root of 6375 (∛6375). We start by labeling the parts of ∛6375 so it is easy to follow along:
∛6375 = 1∛6375 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 6375 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 6375, we first find the greatest perfect cube from the list of factors of 6375. The factors of 6375 are 1, 3, 5, 15, 17, 25, 51, 75, 85, 125, 255, 375, 425, 1275, 2125, and 6375.
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 6375, we divide 6375 by 125, which gives us 51.
To find the simplified coefficient of the radical (c) in the cube root of 6375, we take the cube root of 125, which gives us 5.
That is how you simplify the cube root of 6375. Therefore, the cube root of 6375 in its simplest radical form is as follows:
∛6375 = 5∛51
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