Here we will explain how to simplify the cube root of 34375 (∛34375). We start by labeling the parts of ∛34375 so it is easy to follow along:
∛34375 = 1∛34375 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 34375 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 34375, we first find the greatest perfect cube from the list of factors of 34375. The factors of 34375 are 1, 5, 11, 25, 55, 125, 275, 625, 1375, 3125, 6875, and 34375.
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 34375, we divide 34375 by 125, which gives us 275.
To find the simplified coefficient of the radical (c) in the cube root of 34375, we take the cube root of 125, which gives us 5.
That is how you simplify the cube root of 34375. Therefore, the cube root of 34375 in its simplest radical form is as follows:
∛34375 = 5∛275
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