How To Find Cube Root: Step-By-Step Guide With Examples

cube root

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The cube root of a number is a value that, when raised to the power of three, gives the original number. For example, the cube root of 8 is 2, since 2^3 = 8.

To find the cube root of a number, you can use a calculator or do it by hand using the following steps:

1. Estimate the cube root by finding the closest perfect cube that is less than the given number.
2. Divide the given number by the estimate.
3. Take the average of the estimate and the result of the division.
4. Repeat steps 2 and 3 until you get a desired level of accuracy.

For example, to find the cube root of 27:

1. The closest perfect cube less than 27 is 8 (since 2^3 = 8 and 3^3 = 27).
2. Divide 27 by 8 to get 3.375.
3. Take the average of 8 and 3.375 to get 5.1875.
4. Divide 27 by 5.1875 to get 5.2016, which is closer to the actual cube root.
5. Take the average of 5.1875 and 5.2016 to get 5.1945, which is a good approximation for the cube root of 27 (the actual value is approximately 3.00).

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