Simplify Decimal to Radical Decimal to Radical Algorithm

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SUMMARY

The discussion focuses on the algorithm for converting decimal numbers into their simplified radical forms. A specific method mentioned involves using continued fractions to approximate a decimal number as a radical expression, specifically in the form of sqrt(a/b), where a and b are integers. The tool "Ries" is referenced as a helpful resource for this conversion, particularly with the command "ries 5.1425631813 -NCS" to avoid trigonometric functions. Users are encouraged to explore this method further for effective results.

PREREQUISITES
  • Understanding of decimal and radical forms in mathematics
  • Familiarity with continued fractions
  • Basic knowledge of algorithms
  • Experience with mathematical software tools, specifically "Ries"
NEXT STEPS
  • Research the properties of continued fractions and their applications in approximating decimals
  • Learn how to use the "Ries" algorithm for converting decimals to radicals
  • Explore advanced techniques in number theory related to radical simplification
  • Study examples of decimal to radical conversions to solidify understanding
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Mathematicians, educators, students studying number theory, and anyone interested in algorithms for converting decimal numbers to their radical forms.

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decimal to radical algorithm?

does anyone know if there is a method of writing a decimal number in its simplified radical form?? I really would like to know if there is
 
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do you mean find a radical that is close to a fraction of whole numbers that would approximate the decimal number?

E.g. find a & b such that sqrt(a/b) aprox = C where a &b are integers and C is a decimal.

In that case I don't know. But there exists an algorythm, I have seen it I think on "ask Dr. Math" or something similar.
 
Put it into continued fraction form. You may be able to recognize a repeating portion. (Actually, in trying this myself, I couldn't recognize anything. I'm not quite sure why. Maybe it just takes a whole lot of digits.)

http://home.earthlink.net/~mrob/pub/ries/index.html is your friend. Try "ries 5.1425631813 -NCS" (where -NCS tells ries not to use the sine or cosine functions).
 
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