\(\sqrt{\dfrac{11}{540}}\)
\(=\dfrac{\sqrt{11}}{\sqrt{540}}\)
\(=\dfrac{\sqrt{11}}{\sqrt{6^2\cdot15}}\)
\(=\dfrac{\sqrt{11}}{6\sqrt{15}}\)
\(=\dfrac{\sqrt{11}\cdot\sqrt{15}}{6\sqrt{15}\cdot\sqrt{15}}\)
\(=\dfrac{\sqrt{165}}{6\cdot15}\)
\(=\dfrac{\sqrt{165}}{90}\)