Here we will explain how to simplify the cube root of 17303 (∛17303). We start by labeling the parts of ∛17303 so it is easy to follow along:
∛17303 = 1∛17303 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 17303 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 17303, we first find the greatest perfect cube from the list of factors of 17303. The factors of 17303 are 1, 11, 13, 121, 143, 1331, 1573, and 17303.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 1331 (11 times 11 times 11 equals 1331).
To find the simplified radicand (r) in the cube root of 17303, we divide 17303 by 1331, which gives us 13.
To find the simplified coefficient of the radical (c) in the cube root of 17303, we take the cube root of 1331, which gives us 11.
That is how you simplify the cube root of 17303. Therefore, the cube root of 17303 in its simplest radical form is as follows:
∛17303 = 11∛13
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