how do you find the cubed root of a number?

And if the number is not a perfect cube, you can try different decimals and adjust until you get an accurate enough approximation or us a special algorithm.

If you just need to simplify cube-root expressions yo just need to find the largest cube y^{3
}that is a factor of n and write n = y^{3}x. Then Cuberoot[n] = y*Cuberoot[x]. Example: Cuberoot[192] = Cuberoot[64*3] = Cuberoot[4^{3}*3] = 4*Cuberoot[3].

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Example of the nth root algorithm applied to approximating cube-root of 75834.632

See if you can follow this:

4 2. 3 2 ...

75834.632000000...

64 = 4^3

11834

10088 = 42^{3}-40^{3}

1746632

1598967 = 423^{3}-420^{3}

147665000

107408168 = 4232^{3}-4230^{3}

40256832 etc.