I go ahead and answer the question of 'what is the square root algorithm'. Before we look at this one of many algorithms from real analysis. I'll go through a sample computation and run through the square root algorithm steps without a calculator. After looking at the square root process and giving a nod to an intuitive geometric idea behind taking the square root, I will present a more rigorous version of the algorithm and with the help of the proof of the existence of square roots and the Monotone Convergence Theorem for Real Valued Sequences, provide a sketch of the proof for the algorithms limiting ability to provide the value of the square root of an arbitrary real number.

Skip to Geometric intiution: 5:20
Skip to Algorithm Breakdown: 6:51


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