Here we will explain how to simplify the cube root of 34304 (∛34304). We start by labeling the parts of ∛34304 so it is easy to follow along:
∛34304 = 1∛34304 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 34304 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 34304, we first find the greatest perfect cube from the list of factors of 34304. The factors of 34304 are 1, 2, 4, 8, 16, 32, 64, 67, 128, 134, 256, 268, 512, 536, 1072, 2144, 4288, 8576, 17152, and 34304.
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 34304, we divide 34304 by 512, which gives us 67.
To find the simplified coefficient of the radical (c) in the cube root of 34304, we take the cube root of 512, which gives us 8.
That is how you simplify the cube root of 34304. Therefore, the cube root of 34304 in its simplest radical form is as follows:
∛34304 = 8∛67
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