1. Nov 1, 2012

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!

2. Nov 1, 2012

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.

3. Nov 1, 2012

hammonjj

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)?

$\sqrt{f(x)}$

4. Nov 1, 2012

micromass

Staff Emeritus
You should demand a to be positive as well.

5. Nov 1, 2012

arildno

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

6. Nov 2, 2012

HallsofIvy

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

7. Nov 2, 2012

Erland

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

8. Nov 2, 2012

arildno

Only if I am polite.

9. Nov 2, 2012

Bacle2

Maybe you're looking for something like this:

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