Here we will explain how to simplify the cube root of 324 (∛324). We start by labeling the parts of ∛324 so it is easy to follow along:
∛324 = 1∛324 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 324 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 324, we first find the greatest perfect cube from the list of factors of 324. The factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324.
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 324, we divide 324 by 27, which gives us 12.
To find the simplified coefficient of the radical (c) in the cube root of 324, we take the cube root of 27, which gives us 3.
That is how you simplify the cube root of 324. Therefore, the cube root of 324 in its simplest radical form is as follows:
∛324 = 3∛12
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