Question

 $sqrt{3-sqrt{3+sqrt{11}}} * sqrt{3+sqrt{3+sqrt{11}}} *sqrt{6+sqrt{11}}$

Answer 1

$\sqrt{3-sqrt{3+sqrt{11}}} cdot sqrt{3+sqrt{3+sqrt{11}}} cdot sqrt{6+sqrt{11}}=\ sqrt{(3-sqrt{3+sqrt{11}})(3+sqrt{3+sqrt{11}})(6+sqrt{11})}=\ sqrt{(9-(3+sqrt{11}))(6+sqrt{11})}=\ sqrt{(6-sqrt{11})(6+sqrt{11})}=\ sqrt{36-11}=\ sqrt{25}=\5$