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JAMB 2018 · UTME · Q3

Simplify 22−32+3\dfrac{2\sqrt2 - \sqrt3}{\sqrt2 + \sqrt3}.

Worked solution (try it first)
  1. Multiply the top and bottom by 3−2\sqrt3 - \sqrt2, so the bottom becomes (3+2)(3−2)=3−2(\sqrt3 + \sqrt2)(\sqrt3 - \sqrt2) = 3 - 2, which is 1.
  2. Top: (22−3)(3−2)=26−4−3+6(2\sqrt2 - \sqrt3)(\sqrt3 - \sqrt2) = 2\sqrt6 - 4 - 3 + \sqrt6.
  3. Collect like terms: 36−73\sqrt6 - 7, option B.

Also set as JAMB 2014 · UTME · Q8

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