1．
\((1)\)化简：\( \sqrt{ \dfrac{25}{81}}= \) \(; \sqrt{3 \dfrac{1}{16}}= \) \(; \sqrt{ \dfrac{3}{4}}= \) \(; \sqrt{ \dfrac{a{b}^{5}}{{c}^{2}}}= \)
\((2)\)当\(x\)__________时，式子\( \sqrt{-{\left(x-1\right)}^{2}} \)有意义。
\((3)\)面积为\(S\)且两条邻边的比为\(2\)：\(3\)的长方形的长为_____________，宽为___________．
\((4)\)若\(\sqrt{{28}n}\)是整数，则满足条件的最小正整数\(n\)为______．
\((5)\)观察下列各式：\(① \sqrt{1+ \dfrac{1}{3}}=2 \sqrt{ \dfrac{1}{3}} \)，\(② \sqrt{2+ \dfrac{1}{4}}=3 \sqrt{ \dfrac{1}{4}} ③ \sqrt{3+ \dfrac{1}{5}}=4 \sqrt{ \dfrac{1}{5}} \)，\(……\)请用含\(n(n\geqslant 1)\)的式子写出你猜想的规律：____________________．