[tex]\dfrac{x}{\overline{ab}} = \dfrac{\overline{abab}}{101}\\ \\ \dfrac{x}{\overline{ab}} = \dfrac{100\overline{ab}+\overline{ab}}{101} \\ \\ \dfrac{x}{\overline{ab}} = \dfrac{101\overline{ab}}{101}\\ \\ \dfrac{x}{\overline{ab}} =\overline{ab}\\ \\ x = \overline{ab}^2 \\ \\ \Rightarrow \sqrt x = \overline{ab}[/tex]
