Question

Answer 1

2.\(=\dfrac{\sqrt{5}\left(2-\sqrt{5}\right)}{\sqrt{5}}+\dfrac{4}{\sqrt{5}+1}+\sqrt{\left(2\sqrt{5}-1\right)^2}\)

=\(2-\sqrt{5}+\dfrac{4}{\sqrt{5}+1}+2\sqrt{5}-1\)=\(1+\sqrt{5}+\dfrac{4}{\sqrt{5}+1}\)

\(=\dfrac{\left(1+\sqrt{5}\right)^2+4}{\sqrt{5}+1}=\dfrac{1+2\sqrt{5}+5+4}{\sqrt{5}+1}\)=\(\dfrac{10+2\sqrt{5}}{\sqrt{5}+1}\)

=\(\dfrac{2\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}+1}=2\sqrt{5}\)

4.=\(4-\sqrt{11}+\sqrt{2\left(10+3\sqrt{11}\right)}\)

=\(4-\sqrt{11}+\sqrt{20+6\sqrt{11}}\)=\(4-\sqrt{11}+\sqrt{\left(3+\sqrt{11}\right)^2}\)

\(4-\sqrt{11}+3+\sqrt{11}=7\)