I know that under the radical, we can break it down to smaller radicals or simply into whole numbers if it's a perfect square.

But, with this problem::
radical x^2-1
is it broken down separately?. if so.. the x^2 would become x, but the -1 cant...

my question is, is this the simplest form it can be or can I simply it even more? If so, how can I simplify it even more?:confused:

I assume what you mean is this:

\sqrt {x^2 -1}


and not this:

\sqrt {x^2} \ -\ 1


Is that right? In that case you are correct - there's really nothing more you can do to simplify the expression. If it's the latter that you meant, then what you have is the square root of x squared, so it would be easily simplified as follows:


\sqrt {x^2}\ -\ 1\ =\ x - 1