Simplify Decimal to Radical Decimal to Radical Algorithm

In summary, there is a method for writing a decimal number in its simplified radical form, but it involves converting the number into continued fraction form and potentially recognizing a repeating portion. Another helpful resource is the "ries" function, which can assist in finding a simplified radical form.
  • #1
Zerobu
5
0
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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  • #2
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.
 
  • #3
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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1. What is a decimal to radical algorithm?

A decimal to radical algorithm is a mathematical process used to convert a decimal number into a simplified radical form. It involves finding the factors of the number and writing them as a product of radicals.

2. Why is it important to convert decimals to radicals?

Converting decimals to radicals can help in simplifying complex expressions and solving equations involving radicals. It also makes it easier to compare and perform operations on numbers expressed in radical form.

3. How do you convert a decimal to a radical using the algorithm?

The algorithm involves the following steps:

  • Step 1: Find the factors of the decimal number.
  • Step 2: Write the factors as a product of radicals.
  • Step 3: Simplify the radicals by finding perfect squares.

4. Can any decimal number be converted to a radical form?

No, not all decimal numbers can be converted to a radical form. The number must have a rational square root in order for it to be expressed in radical form. Otherwise, it will remain in decimal form.

5. Are there any shortcuts or tricks for converting decimals to radicals?

Yes, there are some common patterns and rules that can help in simplifying the process of converting decimals to radicals. For example, if the decimal has a perfect square as a factor, it can be written as the square root of that number. Also, if the decimal has a perfect cube as a factor, it can be written as the cube root of that number.

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