How to convert the root of equation in Mathematica

[kaizen.moto]

Hi all,
How to convert the root of an equation from symbolic form into an ordinary from? I have tried to use the N command, but still displaying in the symbolic form.

Thanks

 

[Bill Simpson]

Root[] objects are sometimes returned for complicated roots of higher degree polynomials.

Sometimes, but no always, ToRadicals[] can convert Root[] objects into usually much more complicated nested radicals and get closer to what I think you would consider "ordinary form", but you still have variables in those expressions and that is going to make it more difficult or impossible to get an answer like 3.64.

Unfortunately, after typing your data back in it looks like ToRadicals cannot help you with this one.

All your lambda do appear to even powers. Sometimes you can make a little more progress by substituting z=lambda^2 and working on z instead. Then after you are done you can look at the two square roots of z. Unfortunately this doesn't seem to help in this case either.

 

[Bill Simpson]

I gave this one more try.

All your variables, m, n, a and lambda appear as even powers. Divide all exponents on your variables by 2. If I haven't made any mistakes typing this back in, that gives you a cubic in lambda and reduces the other variable exponents enough that Solve[eqn==0,lambda] is able to recognize it can give you the three roots of the cubic and not use Root[] objects. Then multiply the exponents on m, n and a by two, find the two square roots of each of those three roots of the cubic and you should have the six roots of your original polynomial in lambda.

But that is still going to leave you with all the m, n and a variables in those six roots.

 

[kaizen.moto]

thanks for your comments...i really appreciate it...

 

[alphy]

for your help!

There are a few different methods you can use in Mathematica to convert the root of an equation from symbolic form into an ordinary form. One option is to use the RootApproximant function, which will give you a numerical approximation of the root. Another option is to use the NRoots function, which will give you a list of numerical approximations for all the roots of an equation. Finally, you can also use the Solve or NSolve functions to find the exact or numerical solutions to an equation. You may need to specify the domain and assumptions for these functions to work properly. I hope this helps!