Here we will explain how to simplify the cube root of 34344 (∛34344). We start by labeling the parts of ∛34344 so it is easy to follow along:
∛34344 = 1∛34344 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 34344 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 34344, we first find the greatest perfect cube from the list of factors of 34344. The factors of 34344 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 53, 54, 72, 81, 106, 108, 159, 162, 212, 216, 318, 324, 424, 477, 636, 648, 954, 1272, 1431, 1908, 2862, 3816, 4293, 5724, 8586, 11448, 17172, and 34344.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 216 (6 times 6 times 6 equals 216).
To find the simplified radicand (r) in the cube root of 34344, we divide 34344 by 216, which gives us 159.
To find the simplified coefficient of the radical (c) in the cube root of 34344, we take the cube root of 216, which gives us 6.
That is how you simplify the cube root of 34344. Therefore, the cube root of 34344 in its simplest radical form is as follows:
∛34344 = 6∛159
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