Here we will explain how to simplify the cube root of 7744 (∛7744). We start by labeling the parts of ∛7744 so it is easy to follow along:
∛7744 = 1∛7744 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 7744 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 7744, we first find the greatest perfect cube from the list of factors of 7744. The factors of 7744 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 121, 176, 242, 352, 484, 704, 968, 1936, 3872, and 7744.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 64 (4 times 4 times 4 equals 64).
To find the simplified radicand (r) in the cube root of 7744, we divide 7744 by 64, which gives us 121.
To find the simplified coefficient of the radical (c) in the cube root of 7744, we take the cube root of 64, which gives us 4.
That is how you simplify the cube root of 7744. Therefore, the cube root of 7744 in its simplest radical form is as follows:
∛7744 = 4∛121
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