Here we will explain how to simplify the cube root of 43664 (∛43664). We start by labeling the parts of ∛43664 so it is easy to follow along:
∛43664 = 1∛43664 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 43664 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 43664, we first find the greatest perfect cube from the list of factors of 43664. The factors of 43664 are 1, 2, 4, 8, 16, 2729, 5458, 10916, 21832, and 43664.
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 43664, we divide 43664 by 8, which gives us 5458.
To find the simplified coefficient of the radical (c) in the cube root of 43664, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 43664. Therefore, the cube root of 43664 in its simplest radical form is as follows:
∛43664 = 2∛5458
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