VMath

1. $$ -\sqrt{221}\pm \left\{\frac{1}{2}\sqrt{34}+\frac{3}{2} \sqrt{26} \right\},\ \sqrt{221}\pm \left\{-\frac{1}{2}\sqrt{34}+\frac{3}{2} \sqrt{26} \right\} \ . $$

2. $$ \frac{32}{15}\sqrt{6}+\frac{103}{9}\pm\frac{16}{45}\sqrt{192+515\sqrt{6}}, \ -\frac{32}{15}\sqrt{6}+\frac{103}{9}\pm \mathbf{i} \frac{16}{45}\sqrt{-192+515\sqrt{6}} \ . $$

3. $$ 12+27\,\sqrt[3]{4}, 12-\frac{27}{2} \sqrt[3]{4} \pm \frac{27}{2}\sqrt{3} \sqrt[3]{4} \mathbf i $$

4. $$ (9/2)\sqrt[3]{2}\pm \sqrt{27\,\sqrt[3]{4}+12} $$

5. $$ \pm \left[-1 + \sqrt{-1+\sqrt{13}/2} \pm \mathbf i \left( \sqrt{1+\sqrt{13}/2} -1 \right) \right], $$