Here we will explain how to simplify the cube root of 752 (∛752). We start by labeling the parts of ∛752 so it is easy to follow along:
∛752 = 1∛752 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 752 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 752, we first find the greatest perfect cube from the list of factors of 752. The factors of 752 are 1, 2, 4, 8, 16, 47, 94, 188, 376, and 752.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 8 (2 times 2 times 2 equals 8).
To find the simplified radicand (r) in the cube root of 752, we divide 752 by 8, which gives us 94.
To find the simplified coefficient of the radical (c) in the cube root of 752, we take the cube root of 8, which gives us 2.
That is how you simplify the cube root of 752. Therefore, the cube root of 752 in its simplest radical form is as follows:
∛752 = 2∛94
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