How do I put $\sqrt{x+1}$ into exponential notation? I think $\sqrt{x+1} = x^{1/2} + 1^{1/2}$. Is this incorrect? Why or why not?

If $\displaystyle\sqrt a+\sqrt b=\sqrt{a+b}$
Squaring either sides 
$\displaystyle\implies (\sqrt a+\sqrt b)^2=a+b\iff 2\sqrt{ab}=0\iff ab=0$
$\implies$ at least one of $a,b$ is zero
So, here $x$ has to be zero
