Question

Answer 1

TA có: \(\frac{\sqrt{5+2\sqrt6}+\sqrt{8-2\sqrt{15}}}{\sqrt{7-2\sqrt{10}}}\)

\(=\frac{\sqrt{\left(\sqrt3+\sqrt2\right)^2}+\sqrt{\left(\sqrt5-\sqrt3\right)^2}}{\sqrt{\left(\sqrt5-\sqrt2\right)^2}}=\frac{\sqrt3+\sqrt2+\sqrt5-\sqrt3}{\sqrt5-\sqrt2}\)

\(=\frac{\sqrt5+\sqrt2}{\sqrt5-\sqrt2}=\frac{\left(\sqrt5+\sqrt2\right)^2}{\left(\sqrt5-\sqrt2\right)\left(\sqrt5+\sqrt2\right)}=\frac{7+2\sqrt{10}}{5-2}=\frac{7+2\sqrt{10}}{3}\)