{\sqrt{\sqrt3} \ : \ \sqrt{3}=(3^{\frac{1}{2}})^{\frac{1}{2}}:3^{\frac{1}{2}}=3^{\frac{1}{4}}\ : \ {3^{\frac{1}{2}}}=3^{\frac{1}{4}-\frac{2}{4}}=3^{-\frac{1}{4}}=}
{=\frac{1}{3^{\frac{1}{4}}}=\frac{1}{\sqrt[4]{3}}=\frac{1}{\sqrt[4]{3}}\cdot \frac{\sqrt[4]{3^3}}{\sqrt[4]{3^3}}=\frac{\sqrt[4]{3^3}}{\sqrt[4]{3^4}}=\frac{\sqrt[4]{27}}{3}}