Question

Tính

\(\dfrac{2\sqrt{3}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}+\dfrac{2}{\sqrt{6}+\sqrt{10}}\)

Answer 1

\(\dfrac{2\sqrt{3}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}+\dfrac{2}{\sqrt{6}+\sqrt{10}}\)

=\(\dfrac{2\sqrt{3}\left(\sqrt{6}+\sqrt{10}\right)+2\sqrt{2}+2\sqrt{3}+2\sqrt{5}}{\left(\sqrt{6}+\sqrt{10}\right)\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)}\)

=\(\dfrac{6\sqrt{2}+2\sqrt{30}+2\sqrt{2}+2\sqrt{3}+2\sqrt{5}}{2\sqrt{3}+3\sqrt{2}+\sqrt{30}+2\sqrt{5}+\sqrt{30}+5\sqrt{2}}\)

=\(\dfrac{8\sqrt{2}+2\sqrt{30}+2\sqrt{3}+2\sqrt{5}}{2\sqrt{3}+8\sqrt{2}+2\sqrt{5}+2\sqrt{30}}\)= 1