Here we will explain how to simplify the cube root of 513 (∛513). We start by labeling the parts of ∛513 so it is easy to follow along:
∛513 = 1∛513 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 513 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 513, we first find the greatest perfect cube from the list of factors of 513. The factors of 513 are 1, 3, 9, 19, 27, 57, 171, and 513.
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 513, we divide 513 by 27, which gives us 19.
To find the simplified coefficient of the radical (c) in the cube root of 513, we take the cube root of 27, which gives us 3.
That is how you simplify the cube root of 513. Therefore, the cube root of 513 in its simplest radical form is as follows:
∛513 = 3∛19
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