Here we will explain how to simplify the cube root of 14796 (∛14796). We start by labeling the parts of ∛14796 so it is easy to follow along:
∛14796 = 1∛14796 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 14796 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 14796, we first find the greatest perfect cube from the list of factors of 14796. The factors of 14796 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 137, 274, 411, 548, 822, 1233, 1644, 2466, 3699, 4932, 7398, and 14796.
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 14796, we divide 14796 by 27, which gives us 548.
To find the simplified coefficient of the radical (c) in the cube root of 14796, we take the cube root of 27, which gives us 3.
That is how you simplify the cube root of 14796. Therefore, the cube root of 14796 in its simplest radical form is as follows:
∛14796 = 3∛548
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