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Discussion: Research Area
Topic: Square roots/cube root by subtraction


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Subject:   Square roots/cube root by subtraction
Author: Sonny
Date: May 26 2004
I taught my two sons, when young, the Pythagorean generation of numbers from
counting
tokens, such as bottle caps. Later I taught this to Kindergarten and Elementary
School children.
In particular, generating squares of natural numbers or integers by succesively
adding odd
numbers. I discuss this ONLINE in the file,
http://members.fortunecity.com/jonhays/sqrdots.htm.
This also shows how to find square roots by subtraction, which (as I've found)
can be easily
taught to children. This file hyperlinks to a file,
http://.../jonhays/shortcut.htm , showing how
to simplify the subtraction process. Thus, since 1225 = 35 x 35, this shortcut
reduces the
subtractions from 35 to only 3 + 5 = 8.--In the file,
http://.../jonhays/gentrik.htm , I show how
cubes are generated by a running-sum of odd numbers, and how to use this to
find cube roots. Then
I ask if this suggests any way to extend addition-subtraction to fourth
power/roots and higher.

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