A-level Mathematics/OCR/C1/Indices and Surds/Solutions

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These are the solutions to Indices and Surd Problems.

Indices[edit]

  1. x^5
  2. x
  3. x^3
  4. \frac{1}{x^4}
  5. x^{12}
  6. x^2y^2
  7. \frac{y^3}{b^3}
  8. \sqrt[3]{x^2}
  9. x^2
  10. 1

Surds[edit]

  1. 3
  2. 5
  3. 3\sqrt{5}
  4. 3\sqrt{7}
  5. 10
  6. 4\sqrt{3}
  7. 7\sqrt{2}
  8. 5\sqrt{3}
  9. 4\sqrt{2}
  10. 8\sqrt{5}
  11. 16
  12. \frac{1}{2}
  13. \sqrt[3]{\frac{27}{125}} = \frac{27^\frac{1}{3}}{125^\frac{1}{3}} = \frac{3}{5} (Note: x^\frac{1}{3} \times x^\frac{1}{3} \times x^\frac{1}{3}=x)
  14. \sqrt{\frac{162}{200}} = \frac{\sqrt{162}}{\sqrt{200}} = \frac{\sqrt{81}\times\sqrt{2}}{\sqrt{100}\times\sqrt{2}} = \frac{9\sqrt{2}}{10\sqrt{2}} = \frac{9}{10}
  15. 5
  16. \frac{\sqrt{14}}{3}
  17. 1 (denominator is already rational)
  18. - \frac{32 - 8\sqrt{26}}{10}
  19. \frac{144 + 24\sqrt{19}}{68}
  20. \frac{9 + 3\sqrt{65}}{-56}
  21. \frac{3}{4}
  22. \frac{{a^2}-a\sqrt{a}} {a-1}