Here we will explain how to simplify the cube root of 39000 (∛39000). We start by labeling the parts of ∛39000 so it is easy to follow along:
∛39000 = 1∛39000 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 39000 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 39000, we first find the greatest perfect cube from the list of factors of 39000. The factors of 39000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 25, 26, 30, 39, 40, 50, 52, 60, 65, 75, 78, 100, 104, 120, 125, 130, 150, 156, 195, 200, 250, 260, 300, 312, 325, 375, 390, 500, 520, 600, 650, 750, 780, 975, 1000, 1300, 1500, 1560, 1625, 1950, 2600, 3000, 3250, 3900, 4875, 6500, 7800, 9750, 13000, 19500, and 39000.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 1000 (10 times 10 times 10 equals 1000).
To find the simplified radicand (r) in the cube root of 39000, we divide 39000 by 1000, which gives us 39.
To find the simplified coefficient of the radical (c) in the cube root of 39000, we take the cube root of 1000, which gives us 10.
That is how you simplify the cube root of 39000. Therefore, the cube root of 39000 in its simplest radical form is as follows:
∛39000 = 10∛39
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