Question

\(\sqrt{5}\left(\sqrt{6}+1\right):\frac{\sqrt{2\sqrt{3}+\sqrt{2}}}{\sqrt{2\sqrt{3}-\sqrt{2}}}\)

Answer 1

\(=\sqrt{5}\left(\sqrt{6}+1\right).\frac{\sqrt{2\sqrt{3}-\sqrt{2}}}{\sqrt{2\sqrt{3}+\sqrt{2}}}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\)

\(=\sqrt{5}\left(\sqrt{6}+1\right).\frac{\sqrt{\sqrt{2}\left(\sqrt{6}-1\right)}}{\sqrt{\sqrt{2}\left(\sqrt{6}+1\right)}}\)

\(=\frac{\sqrt{5}\left(\sqrt{\sqrt{6}+1}\right)^2.\sqrt{\sqrt{2}}.\sqrt{\sqrt{6}-1}}{\sqrt{\sqrt{2}}.\sqrt{\sqrt{6}+1}}\)

\(=\sqrt{5}\left(\sqrt{\sqrt{6}+1}\right)\sqrt{\sqrt{6}-1}\)

\(=\sqrt{5}.\sqrt{6-1}\)

=\(\sqrt{5}.\sqrt{5}\)

\(=5\)

Answer 2

\(\sqrt{5}\left(\sqrt{6}+1\right):\frac{\sqrt{2\sqrt{3}+\sqrt{2}}}{\sqrt{2\sqrt{3}-\sqrt{2}}}\)