Question

Answer 1

\(E=\sqrt{5+2\sqrt{5}+1}-\dfrac{\sqrt{3}\left(\sqrt{5}-1\right)}{\sqrt{3}}\\ =\sqrt{\left(\sqrt{5}+1\right)^2}-\sqrt{5}+1\\ =\left|\sqrt{5}+1\right|-\sqrt{5}+1\\ =\sqrt{5}+1-\sqrt{5}+1\\ =2\)

Answer 2

\(E=\sqrt{6+2\sqrt{5}}-\dfrac{\sqrt{15}-\sqrt{3}}{\sqrt{3}}\)

\(=\sqrt{\left(\sqrt{5}\right)^2+2\sqrt{5}+1}-\dfrac{\sqrt{15}}{\sqrt{3}}+\dfrac{\sqrt{3}}{\sqrt{3}}\)

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

\(=\sqrt{5}+1-\sqrt{5}+1=2\left(vì\sqrt{5}+1>0\right)\)