Here we will explain how to simplify the cube root of 5165 (∛5165). We start by labeling the parts of ∛5165 so it is easy to follow along:
∛5165 = 1∛5165 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 5165 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 5165, we first find the greatest perfect cube from the list of factors of 5165. The factors of 5165 are 1, 5, 1033, and 5165.
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 5165, we divide 5165 by 1, which gives us 5165.
To find the simplified coefficient of the radical (c) in the cube root of 5165, we take the cube root of 1, which gives us 1.
That is how you simplify the cube root of 5165. Therefore, the cube root of 5165 in its simplest radical form is as follows:
∛5165 = ∛5165
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