From Förberedande kurs i matematik 1

Because \displaystyle \sqrt{3} is \displaystyle 3^{\frac{1}{2}}, then \displaystyle \sqrt{\sqrt{3}}=\sqrt{3^{{1}/{2}\;}}=\left( 3^{{1}/{2}\;} \right)^{{1}/{2}\;}=3^{\frac{1}{2}\centerdot \frac{1}{2}}=3^{{1}/{4}\;}