Question

Tính:

\(\dfrac{\sqrt{5+2\sqrt{6}}+\sqrt{8-2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)

Answer 1

\(\dfrac{\sqrt{5+2\sqrt{6}}+\sqrt{8-2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}=\dfrac{\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}}{\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}}\)

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

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