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JAMB 2010 · UTME · Q9

Rationalise 23+55−3\dfrac{2\sqrt3 + \sqrt5}{\sqrt5 - \sqrt3}.

Worked solution (try it first)
  1. Multiply the top and bottom by the conjugate of the bottom, 5+3\sqrt5 + \sqrt3.
  2. Bottom: (5−3)(5+3)=5−3(\sqrt5 - \sqrt3)(\sqrt5 + \sqrt3) = 5 - 3, which is 2.
  3. Top: (23+5)(5+3)=215+6+5+15(2\sqrt3 + \sqrt5)(\sqrt5 + \sqrt3) = 2\sqrt{15} + 6 + 5 + \sqrt{15}, which is 315+113\sqrt{15} + 11.
  4. So the value is 315+112\dfrac{3\sqrt{15} + 11}{2}, option A.

Also set as JAMB 2016 · UTME · Q21

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