Recently I attended an interview and among the other problem-solving questions, I was asked to estimate the square root of 1, 000. Following a rational trial-and-error approach trying to bound the solution, I managed to estimate that the square root of 1, 000 is 31.6. Immediately after the interview, I was puzzled about how the square root of a number can be calculated by hand. After a quick Google search, I found a number of links demonstrating how to calculate the square or cube root of a number by hand. My instant reaction was to try to understand the method and prove how the steps are derived. Once that was achieved, I was interested to find out how I can generalise the method and make it applicable to calculate by hand the root of any order of any number.
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