Here we will explain how to simplify the cube root of 34398 (∛34398). We start by labeling the parts of ∛34398 so it is easy to follow along:
∛34398 = 1∛34398 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 34398 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 34398, we first find the greatest perfect cube from the list of factors of 34398. The factors of 34398 are 1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 27, 39, 42, 49, 54, 63, 78, 91, 98, 117, 126, 147, 182, 189, 234, 273, 294, 351, 378, 441, 546, 637, 702, 819, 882, 1274, 1323, 1638, 1911, 2457, 2646, 3822, 4914, 5733, 11466, 17199, and 34398.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 27 (3 times 3 times 3 equals 27).
To find the simplified radicand (r) in the cube root of 34398, we divide 34398 by 27, which gives us 1274.
To find the simplified coefficient of the radical (c) in the cube root of 34398, we take the cube root of 27, which gives us 3.
That is how you simplify the cube root of 34398. Therefore, the cube root of 34398 in its simplest radical form is as follows:
∛34398 = 3∛1274
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