2

In[28]:=

Nest[# - (#^2 - 10.)/(2#) &, 3., 10]

10^(1/2)//N

Out[28]=

3.16228

Out[29]=

3.16228

In[30]:=

FixedPoint[# - (#^2 - 10.)/(2#) &, 3.]

Out[30]=

3.16228

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