WAEC 2023 · Paper 1 · Q1

Express $\dfrac{3}{3 - \sqrt{6}}$ in the form $x + m\sqrt{y}$ .

Worked solution (try it first)

Multiply the top and bottom by the conjugate $3 + \sqrt{6}$ to clear the surd from the bottom.
The bottom becomes $3^2 - (\sqrt{6})^2 = 9 - 6 = 3$ , and the top becomes $3(3 + \sqrt{6})$ .
Cancel the 3: $\dfrac{3(3 + \sqrt{6})}{3} = 3 + \sqrt{6}$ , option B.