WAEC 2020 · Paper 1 · Q7

Simplify: $\dfrac{\sqrt{5} + 3}{4 - \sqrt{10}}$ .

Worked solution (try it first)

Multiply top and bottom by the conjugate $4 + \sqrt{10}$ .
The bottom becomes $16 - 10 = 6$ .
Expand the top: $(\sqrt{5} + 3)(4 + \sqrt{10}) = 4\sqrt{5} + \sqrt{50} + 12 + 3\sqrt{10}$ , and $\sqrt{50} = 5\sqrt{2}$ .
Divide each term by 6: $\frac{4}{6}\sqrt{5} + \frac{5}{6}\sqrt{2} + 2 + \frac{3}{6}\sqrt{10}$ .
So the answer is $\frac{2}{3}\sqrt{5} + \frac{5}{6}\sqrt{2} + \frac{1}{2}\sqrt{10} + 2$ , option C.