\(\sqrt{\dfrac{\left(1-\sqrt{3}\right)^2}{27}}=\dfrac{\sqrt{\left(\sqrt{3}-1\right)^2}}{\sqrt{27}}=\dfrac{\sqrt{3}-1}{\sqrt{27}}=\dfrac{\sqrt{27}\left(\sqrt{3}-1\right)}{27}=\dfrac{9-3\sqrt{3}}{27}=\dfrac{3\left(3-\sqrt{3}\right)}{27}=\dfrac{3-\sqrt{3}}{9}\)