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?

$$
9^{1/2} + 16^{1/2} = 3 + 4 = 7 \ne 5 = 25^{1/2} = (9+16)^{1/2}.
$$
So
$$
\left(\frac{9}{16}\right)^{1/2} + 1^{1/2} = \frac 3 4 + 1 = \frac 7 4 \ne \frac 5 4 = \left(\frac{25}{16}\right)^{1/2} = \left(\frac{9}{16}+1\right)^{1/2}
$$
In other words, if $x=\dfrac{9}{16}$ then $x^{1/2}+1^{1/2}$ is not at all the same as $(x+1)^{1/2}$.
