WAEC 2022 · Paper 1 · Q2

Simplify: $\left(\dfrac{3\sqrt{6} + \sqrt{54}}{\sqrt{5}\left(3\sqrt{5}\right)}\right)^{-1}$ .

Worked solution (try it first)

Simplify the surd: $\sqrt{54} = \sqrt{9 \times 6} = 3\sqrt{6}$ , so the top is $3\sqrt{6} + 3\sqrt{6} = 6\sqrt{6}$ .
The bottom is $3 \times \sqrt{5} \times \sqrt{5} = 3 \times 5$
$= 15$ , so the fraction is $\dfrac{6\sqrt{6}}{15} = \dfrac{2\sqrt{6}}{5}$ .
The power $-1$ turns the fraction upside down: $\dfrac{5}{2\sqrt{6}}$ .
Rationalise by multiplying top and bottom by $\sqrt{6}$ : $\dfrac{5\sqrt{6}}{2 \times 6} = \dfrac{5\sqrt{6}}{12}$ , option C.