How does sqrt(x-3)^2=x-3?

How does sqrt(x-3)^2=x-3?

1.
$\begin{array}{|rcll|} \hline \sqrt{(x-3)^2} &=& \left(~ \sqrt{x-3} ~ \right)^2 \\ \hline \end{array}$

2.

$\begin{array}{|rcll|} \hline \sqrt{x-3} &=& (x-3)^{\frac12} \\ \hline \end{array}$

3.

$\begin{array}{|rcll|} \hline \sqrt{(x-3)^2} &=& \left( ~ \sqrt{x-3} ~ \right)^2 \\ &=& \left( ~ (x-3)^{\frac12} ~ \right)^2 \\ &=& (x-3)^{\frac12\cdot 2} \\ &=& (x-3)^{\frac22 } \\ &=& (x-3)^{1} \\ &=& (x-3) \\ \hline \end{array}$