Question

 

Answer 1

\(\sqrt{14}\)

Answer 2

\(\sqrt{5+\sqrt{11}}.\sqrt{5-\sqrt{11}}=\sqrt{\left(5+\sqrt{11}\right)\left(5-\sqrt{11}\right)}\)

\(=\sqrt{25-11}=\sqrt{14}\)

Answer 3

\(\sqrt{5+\sqrt{11}}\cdot\sqrt{5-\sqrt{11}}=\sqrt{\left(5+\sqrt{11}\right)\cdot\left(5-\sqrt{11}\right)}\)

\(=\sqrt{5^2-\left(\sqrt{11}\right)^2}=\sqrt{25-11}=\sqrt{14}\)