Here we will explain how to simplify the cube root of 4802 (∛4802). We start by labeling the parts of ∛4802 so it is easy to follow along:
∛4802 = 1∛4802 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 4802 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 4802, we first find the greatest perfect cube from the list of factors of 4802. The factors of 4802 are 1, 2, 7, 14, 49, 98, 343, 686, 2401, and 4802.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 343 (7 times 7 times 7 equals 343).
To find the simplified radicand (r) in the cube root of 4802, we divide 4802 by 343, which gives us 14.
To find the simplified coefficient of the radical (c) in the cube root of 4802, we take the cube root of 343, which gives us 7.
That is how you simplify the cube root of 4802. Therefore, the cube root of 4802 in its simplest radical form is as follows:
∛4802 = 7∛14
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