Here we will explain how to simplify the cube root of 6750 (∛6750). We start by labeling the parts of ∛6750 so it is easy to follow along:
∛6750 = 1∛6750 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 6750 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 6750, we first find the greatest perfect cube from the list of factors of 6750. The factors of 6750 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 125, 135, 150, 225, 250, 270, 375, 450, 675, 750, 1125, 1350, 2250, 3375, and 6750.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 3375 (15 times 15 times 15 equals 3375).
To find the simplified radicand (r) in the cube root of 6750, we divide 6750 by 3375, which gives us 2.
To find the simplified coefficient of the radical (c) in the cube root of 6750, we take the cube root of 3375, which gives us 15.
That is how you simplify the cube root of 6750. Therefore, the cube root of 6750 in its simplest radical form is as follows:
∛6750 = 15∛2
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