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At present there does not exist a long hand method for finding the higher roots (say 4th , 5th etc.) of a positive real number.
The formula suggested here, enables us to find any root of a positive real number. With or without decimal.
Re: How to Calculate The nth root of a positive real number
This is a great discovery in the field of pure mathematics.The long hand method given in the book must be included in the text books for the benefit of the scholers.