NECO 2022 · Paper 1 · Q16

Simplify $\dfrac{3}{\sqrt{3} + 6}$ .

Worked solution (try it first)

Multiply the top and bottom by the conjugate $6 - \sqrt{3}$ .
The bottom becomes $6^2 - (\sqrt{3})^2 = 36 - 3 = 33$ and the top becomes $3(6 - \sqrt{3})$ .
Cancel 3: $\dfrac{6 - \sqrt{3}}{11}$ , option B.