JAMB 2014 · UTME · Q20

What is the common ratio of the G.P. $(\sqrt{10} + \sqrt5), (\sqrt{10} + 2\sqrt5), \ldots$ ?

Worked solution (try it first)

The common ratio is the second term divided by the first: $r = \dfrac{\sqrt{10} + 2\sqrt5}{\sqrt{10} + \sqrt5}$ .
Since $\sqrt{10} = \sqrt2\sqrt5$ , take $\sqrt5$ out of the top and bottom: $r = \dfrac{\sqrt2 + 2}{\sqrt2 + 1}$ .
Write $2 = \sqrt2 \times \sqrt2$ , so the top is $\sqrt2(1 + \sqrt2)$ and cancels with the bottom.
So $r = \sqrt2$ , option B.