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NECO 2024 · Paper 1 · Q9

Rationalize 52+3\dfrac{5}{\sqrt2 + \sqrt3}.

Worked solution (try it first)
  1. Multiply the top and bottom by 3−2\sqrt3 - \sqrt2.
  2. Bottom: (3+2)(3−2)=3−2(\sqrt3 + \sqrt2)(\sqrt3 - \sqrt2) = 3 - 2, which is 1.
  3. So the value is 5(3−2)5(\sqrt3 - \sqrt2), option A.

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