Three, let $A B C D$ be a square cardboard, and divide it into three rectangles with lines $P Q$ and $R S$ parallel to $B C$,
as shown in the figure. Fold the cardboard so that point $C$ lands on point $C^{\prime}$ on $A B$, and point $S$ lands on point $S^{\prime}$ on $P Q$, and
$B C^{\prime}=1$. Try to find
the length of $A C^{\prime}$.
Three, Hint: Let $A C^{\prime}=x, B T=y$, and note that $C^{\prime} T=C T$. Apply the Pythagorean theorem to Rt $\triangle B C^{\prime} T$ to get an expression for $y$ in terms of $x$, and then consider $\triangle P C^{\prime} S^{\prime} \sim \triangle B T C^{\prime}$ and $C^{\prime} S^{\prime}=C S$, which can give another expression for $y$ in terms of $x$. $A C^{\prime}=3 \sqrt{2}$.