# How do you prove that the square root of a number #S# can be approximated by using the recurrence relation: #x_(n+1) = 1/2(x_n+S/x_n)# ?

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Not sure how to prove this or why it works?

Not sure how to prove this or why it works?

##### 1 Answer

Mar 8, 2016

This is an application of Newton's method.

Let

Then the zeros of