can someone explain to me how sqrt(x^2 + x^4) became sqrt(1+x^2)?
You can factor out an x^2 from the expression under the square root: $\displaystyle \sqrt{x^2(1+x^2)}$ and, by the laws of surds, $\displaystyle \sqrt{x^2}\sqrt{1+x^2} = |x|\sqrt{1+x^2}$
The |x| which is now outside the radical is cancelled with the x in the numerator. (They have said that $\displaystyle \sqrt{x^2} = x$ before cancelling which is OK if x>0[/tex]