Question

Trục căn thức ở mẫu: \(\frac{1}{\sqrt{8}-\sqrt{3}-\sqrt{5}}\)

Answer 1

\(\frac{1}{\sqrt{8}-\sqrt{3}-\sqrt{5}}=\frac{1}{\sqrt{8}-\left(\sqrt{3}+\sqrt{5}\right)}=\frac{\sqrt{8}+\left(\sqrt{3}+\sqrt{5}\right)}{8-\left(\sqrt{3}+\sqrt{5}\right)^2}\)

\(=\frac{\sqrt{8}+\sqrt{3}+\sqrt{5}}{8-\left(3+2\sqrt{3}\sqrt{5}+5\right)}=\frac{\sqrt{8}+\sqrt{3}+\sqrt{5}}{8-8-2\sqrt{15}}\)

\(=\frac{\sqrt{8}+\sqrt{3}+\sqrt{5}}{-2\sqrt{15}}=\frac{\sqrt{15}.\left(\sqrt{8}+\sqrt{3}+\sqrt{5}\right)}{-2.15}=\frac{2\sqrt{30}+3\sqrt{5}+5\sqrt{3}}{-30}\)