Here we will explain how to simplify the cube root of 15750 (∛15750). We start by labeling the parts of ∛15750 so it is easy to follow along:
∛15750 = 1∛15750 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 15750 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 15750, we first find the greatest perfect cube from the list of factors of 15750. The factors of 15750 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 30, 35, 42, 45, 50, 63, 70, 75, 90, 105, 125, 126, 150, 175, 210, 225, 250, 315, 350, 375, 450, 525, 630, 750, 875, 1050, 1125, 1575, 1750, 2250, 2625, 3150, 5250, 7875, and 15750.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 125 (5 times 5 times 5 equals 125).
To find the simplified radicand (r) in the cube root of 15750, we divide 15750 by 125, which gives us 126.
To find the simplified coefficient of the radical (c) in the cube root of 15750, we take the cube root of 125, which gives us 5.
That is how you simplify the cube root of 15750. Therefore, the cube root of 15750 in its simplest radical form is as follows:
∛15750 = 5∛126
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