Consider the problem of finding the square root of a number. Newton's method is one of many methods of computing square roots.
For example, if one wishes to find the square root of 612, this is equivalent to finding the solution to
The function to use in Newton's method is then,
with derivative,
With an initial guess of 10, the sequence given by Newton's method is
where the correct digits are underlined. With only a few iterations one can obtain a solution accurate to many decimal places.
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Square root of a number[edit]
Consider the problem of finding the square root of a number. Newton's method is one of many methods of computing square roots.
For example, if one wishes to find the square root of 612, this is equivalent to finding the solution to
The function to use in Newton's method is then,
with derivative,
With an initial guess of 10, the sequence given by Newton's method is
where the correct digits are underlined. With only a few iterations one can obtain a solution accurate to many decimal places.