Matematika 12

Greg Attwood, Jack Barraclough, Ian Bettison, Alistair Macpherson, Bronwen Moran, Su Nicholson, Diane Oliver, Joe Petran, Keith Bledger, Harry Smith, Geoff Staley, Robert Ward-Penny dhe Dave Wilkins

Pyetja

Racionalizo emëruesit dhe thjeshto:

  1. 11+3\dfrac{1}{1 + \sqrt{3}}
  2. 12+5\dfrac{1}{2 + \sqrt{5}}
  3. 137\dfrac{1}{3 - \sqrt{7}}
  4. 435\dfrac{4}{3 - \sqrt{5}}
  5. 153\dfrac{1}{\sqrt{5} - \sqrt{3}}
  6. 3245\dfrac{3 - \sqrt{2}}{4 - \sqrt{5}}
  7. 52+5\dfrac{5}{2 + \sqrt{5}}
  8. 5287\dfrac{5\sqrt{2}}{\sqrt{8} - \sqrt{7}}
  9. 113+11\dfrac{11}{3 + \sqrt{11}}
  10. 373+7\dfrac{\sqrt{3} - \sqrt{7}}{\sqrt{3} + \sqrt{7}}
  11. 171117+11\dfrac{\sqrt{17} - \sqrt{11}}{\sqrt{17} + \sqrt{11}}
  12. 41+294129\dfrac{\sqrt{41} + \sqrt{29}}{\sqrt{41} - \sqrt{29}}
  13. 2332\dfrac{\sqrt{2} - \sqrt{3}}{\sqrt{3} - \sqrt{2}}