Here we will explain how to simplify the cube root of 87808 (∛87808). We start by labeling the parts of ∛87808 so it is easy to follow along:
∛87808 = 1∛87808 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 87808 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 87808, we first find the greatest perfect cube from the list of factors of 87808. The factors of 87808 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 128, 196, 224, 256, 343, 392, 448, 686, 784, 896, 1372, 1568, 1792, 2744, 3136, 5488, 6272, 10976, 12544, 21952, 43904, and 87808.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 21952 (28 times 28 times 28 equals 21952).
To find the simplified radicand (r) in the cube root of 87808, we divide 87808 by 21952, which gives us 4.
To find the simplified coefficient of the radical (c) in the cube root of 87808, we take the cube root of 21952, which gives us 28.
That is how you simplify the cube root of 87808. Therefore, the cube root of 87808 in its simplest radical form is as follows:
∛87808 = 28∛4
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