Let Q be a non-square intger.
The Bhaskara-Brouncker Algorithm gives successive approximations of √Q as ai/bi, where a0 = b0 = 1, and
ai+1 = ai + biQ
bi+1 = ai + bi
This is the Bhaskara-Brouncker algorithm whose dervation we omit.
Now, setting xi = ai/bi,
we get the following surprising formula for successive approximations to √Q:
xi+1 = (xi + Q)/(xi +1) with x0 = 1.
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