What is the common ratio of the G P sqrt 10 sqr... - JAMB Mathematics 2014 Question

Common ratio r of the G.P is

(r = \frac{T_n + 1}{T_n} = \frac{T_2}{T_1})

(r = \frac{\sqrt{10} + 2\sqrt{5}}{\sqrt{10} + \sqrt{5}})

(r = \frac{\sqrt{10} + 2\sqrt{5}}{\sqrt{10} + \sqrt{5}} \times \frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} - \sqrt{5}} )

( = \frac{(\sqrt{10})(\sqrt{10}) + (\sqrt{10})(-\sqrt{5}) + (2\sqrt{5})(\sqrt{10}) + (2\sqrt{5})(-\sqrt{5})}{(\sqrt{10})^2 - (\sqrt{5})^2})

(\frac{10 - \sqrt{50} + 2\sqrt{50} - 10}{10 - 5})

(\frac{\sqrt{50}}{5})

(\frac{\sqrt{25 \times 2}}{5})

(\frac{5\sqrt{2}}{5})

(\sqrt{2})