Here we will explain how to simplify the cube root of 5120 (∛5120). We start by labeling the parts of ∛5120 so it is easy to follow along:
∛5120 = 1∛5120 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 5120 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 5120, we first find the greatest perfect cube from the list of factors of 5120. The factors of 5120 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2560, and 5120.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 512 (8 times 8 times 8 equals 512).
To find the simplified radicand (r) in the cube root of 5120, we divide 5120 by 512, which gives us 10.
To find the simplified coefficient of the radical (c) in the cube root of 5120, we take the cube root of 512, which gives us 8.
That is how you simplify the cube root of 5120. Therefore, the cube root of 5120 in its simplest radical form is as follows:
∛5120 = 8∛10
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