Math for the people, by the people.

User login

A simple method for finding the roots of numbers

Major Section: 
Education
Type of Math Object: 
Topic

Mathematics Subject Classification

65H04 Roots of polynomial equations

Comments

A simple method for finding the roots of numbers

Dear Peter: I took the liberty of translating your document into LaTeX. I hope I didn’t make any mistakes. Please check it. You should be able to follow the syntax easily enough to make any needed corrections. -Joe

A simple method for finding the roots of numbers

Joe, I also attempted to clarify the text by correcting some exponents, which appeared as factors rather than exponents, and properly representing the fifth root, which previously appeared as five times the square root. I was not wholely successful, as one could now mistake it in some cases as x to the fifth power, rather than ”times the fifth root of.” I was also unsuccessful in adding a space that would have made my meaning clearer. I think you will see what I mean. I am hoping to get this in final form so no more edits are needed, as I want it published for the record. But being as yet unfamiliar with the use of the various softwares on this site, I am at a bit of a disadvantage, so thanks, Joe, for your help.

A simple method for finding the roots of numbers

I also removed a few of the multiplication symbols where they might have been misconstrued as variables, and fixed one more root symbol by raising up the ”5” in front of it so it would not be misconstrued as the factor of 5 and the square root, but rather read: ”the fifth root of.” I think it is in a bit better shape now, but some spaces could be added here and there to make sure numbers in front of the fifth root symbol are not thought to be raised to the fifth power and multiplied by the square root.

A simple method for finding the roots of numbers

\sqrt[5]{243}=3 normal-→\rightarrow 2435=352433\sqrt[5]{243}=3

A simple method for finding the roots of numbers

Thanks again, Joe. I went through the document a few more times and cleaned up some additional messes. Looks a lot better now.

ancient Egyptians, Greeks and medieval used no more than three steps to estimate the square root of 11. Step one guessed (3 + 1/3)^2 , an accuracy of 1/9, good for carpenters.

step two divided 1/9 by 2(3 + 1/3), multiplied 1/9 x 3/20 = 1/60 , MEANT (3 + 1/3 - 1/60)^2 is accurate to 1/3600.

step three divided 1/3600 by 2(3 + 19/60), multiplied 1/3600 x 60/396 = 1/23760 meant (3 + 19/60 -1/23760)^2 is accurate to (1/23760)^2

ancient Egyptians, Greeks and medieval used no more than three steps to estimate the square root of 2. Step one guessed (1 + 2/5)^2 , an accuracy of (1/25), was not good for carpenters.

step 2 divided 1/25 by 2(1 + 2/5) meant 1/25 x 5/14 = 1/70 and (1 + 2/5 + 1/70)^2 was accurate to 1/4900 for carpenters,

step three divided 1/4900 by 2(1 + 29/70), meant 1/4900 x 70/198 = 1/13860 found (1 + 29/70-1 13860)^2 was accurate to (1/13860)^2 9 places in modern decimals

Subscribe to Comments for "A simple method for finding the roots of numbers"
loading