Killing Time Taking Square Roots

My attention was wandering at some meeting or other so I started taking the square root of 6 by hand.  Nothing like an arithmetic algorithm to occupy empty time and keep me calm.  I chose six because it gave me so much trouble using mental math.  I like algorithm so much that I decided to show that it was somehow more efficient that Newton’s method.  Fat chance.

Here is the work by hand.

Square Root of 6 By Hand

Notice how the correct digits appear one by one as the work of multiplying and subtraction also increases by one digit of a time.

Here is Newton’s method.

Square Root of 6 By Newton's Method

For each iteration of the formula,  the accurate digits of the square root double.

In both methods the algorithm ends with a divide-like operations but the work increases on each sub-step by hand and it stays the same (a property of the division algorithm) using Newton’s method and besides the accuracy doubled.  Oh well.


About jrh794

I am a sixty-five year old math instructor at Southern Oregon University. I taught at the College of the Siskiyous in Weed California for twenty-six years. Prior to that I worked as a computer programmer, carpenter and in various other jobs. I graduated from Rice University in 1967 and have a MS in Operations Research from Stanford. In the past I have hand-built a stone house and taken long solo bicycle tours. Now I ride my mountain bike and play golf for recreation.
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