Here we will explain how to simplify the cube root of 15504 (∛15504). We start by labeling the parts of ∛15504 so it is easy to follow along:
∛15504 = 1∛15504 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 15504 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 15504, we first find the greatest perfect cube from the list of factors of 15504. The factors of 15504 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 19, 24, 34, 38, 48, 51, 57, 68, 76, 102, 114, 136, 152, 204, 228, 272, 304, 323, 408, 456, 646, 816, 912, 969, 1292, 1938, 2584, 3876, 5168, 7752, and 15504.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 8 (2 times 2 times 2 equals 8).
To find the simplified radicand (r) in the cube root of 15504, we divide 15504 by 8, which gives us 1938.
To find the simplified coefficient of the radical (c) in the cube root of 15504, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 15504. Therefore, the cube root of 15504 in its simplest radical form is as follows:
∛15504 = 2∛1938
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