Here we will explain how to simplify the cube root of 87480 (∛87480). We start by labeling the parts of ∛87480 so it is easy to follow along:
∛87480 = 1∛87480 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 87480 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 87480, we first find the greatest perfect cube from the list of factors of 87480. The factors of 87480 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 243, 270, 324, 360, 405, 486, 540, 648, 729, 810, 972, 1080, 1215, 1458, 1620, 1944, 2187, 2430, 2916, 3240, 3645, 4374, 4860, 5832, 7290, 8748, 9720, 10935, 14580, 17496, 21870, 29160, 43740, and 87480.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 5832 (18 times 18 times 18 equals 5832).
To find the simplified radicand (r) in the cube root of 87480, we divide 87480 by 5832, which gives us 15.
To find the simplified coefficient of the radical (c) in the cube root of 87480, we take the cube root of 5832, which gives us 18.
That is how you simplify the cube root of 87480. Therefore, the cube root of 87480 in its simplest radical form is as follows:
∛87480 = 18∛15
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