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SMO 2016 Senior Round 1 Question 9

SMO · SMO 2016 Senior Round 1

Question 9

Which of the following is equal to $$\frac 1{\sqrt{2000}+\sqrt{2004}}+\frac 1{\sqrt{2004}+\sqrt{2008}}+\frac 1{\sqrt{2008}+\sqrt{2012}}+\frac 1{\sqrt{2012}+\sqrt{2016}}?$$
  1. $3\sqrt{14}-5\sqrt 5$
  2. $4\sqrt{14}-5\sqrt 5$
  3. $3\sqrt{14}-5\sqrt 3$
  4. $3\sqrt{14}-3\sqrt 5$
  5. $3\sqrt 7-\sqrt 5$