Here we will explain how to simplify the cube root of 13122 (∛13122). We start by labeling the parts of ∛13122 so it is easy to follow along:
∛13122 = 1∛13122 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 13122 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 13122, we first find the greatest perfect cube from the list of factors of 13122. The factors of 13122 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458, 2187, 4374, 6561, and 13122.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 729 (9 times 9 times 9 equals 729).
To find the simplified radicand (r) in the cube root of 13122, we divide 13122 by 729, which gives us 18.
To find the simplified coefficient of the radical (c) in the cube root of 13122, we take the cube root of 729, which gives us 9.
That is how you simplify the cube root of 13122. Therefore, the cube root of 13122 in its simplest radical form is as follows:
∛13122 = 9∛18
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