What is a Radical and How Does it Relate to Bizarre Functions?

[hammonjj]

I'm currently writing a proof that relates to continuity of a bizarre function and I ran across an interesting thought, at least to me. I don't really know what a radical √ is. For example, 6^3 is:

6*6*6

and x^n is:

x*x*x*x*x*x*x*x*x*x, n times, but what is a square root (ie. radical)? It's the opposite of a power, but I don't know how to define it!

Thanks!

 

[arildno]

A number "a" is the square root
of a number "b", if a*a=b.
that's the definition you may work with at present, and it is sufficient for most purposes.

 

[hammonjj]

A number "a" is the square root
of a number "b", if a*a=b.
that's the definition you may work with at present, and it is sufficient for most purposes.

I guess I should be slightly more specific about the work I am doing. What about the radical of a function? Could it be defined as f(x)=g(x)*g(x)?

$\sqrt{f(x)}$

 

[micromass]

A number "a" is the square root
of a number "b", if a*a=b.
that's the definition you may work with at present, and it is sufficient for most purposes.

You should demand a to be positive as well.

 

[arildno]

You should demand a to be positive as well.

"the" is "the (positive)" in Norwegian.
It is not my fault that you are as incompetent in Norwegian as I am in Zulu.

 

[HallsofIvy]

No, but if you expecting Norwegian usages to carry over to Engish, it is.

 

[Erland]

Well, $\sqrt{a}=a^{1/2}$ if $a>0$.

 

[arildno]

No, but if you expecting Norwegian usages to carry over to Engish, it is.

Only if I am polite.

 

[Bacle2]

I guess I should be slightly more specific about the work I am doing. What about the radical of a function? Could it be defined as f(x)=g(x)*g(x)?

$\sqrt{f(x)}$

Maybe you're looking for something like this:

http://en.wikipedia.org/wiki/Functional_calculus ?