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

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Feel free to add more problems as long as you provide the solutions

Contents

Indices[edit]

Simplify the Indices.

  1. x^2x^3
  2. x^3x^{-2}
  3. \frac{x^5}{x^2}
  4. x^{-4}
  5. \left(x^3\right)^4
  6. \left(xy\right)^2
  7. \left(\frac{y}{b}\right)^3
  8. x^{\frac{2}{3}}
  9. \frac{x^2x^4}{\left(x^2\right)^2}
  10. x^5x^{-5}

Surds[edit]

Simplify the following Surds.

  1. \sqrt{9}
  2. \sqrt{25}
  3. \sqrt{45}
  4. \sqrt{63}
  5. \sqrt{100}
  6. \sqrt{48}
  7. \sqrt{98}
  8. \sqrt{75}
  9. \sqrt{32}
  10. \sqrt{320}
  11. \sqrt{256}
  12. \sqrt{\frac{9}{36}}
  13. \sqrt[3]{\frac{27}{125}}
  14. \sqrt{\frac{162}{200}}
  15. \sqrt{\frac{75}{3}}
  16. \sqrt{\frac{112}{72}}

    Rationalize the Denominator

  17. \frac{2}{\sqrt{4}}
  18. \frac{8}{4 + \sqrt{26}}
  19. \frac{12}{12 - \sqrt{76}}
  20. \frac{3}{3 - \sqrt{65}}
  21. \frac{9}{9 + \sqrt{9}}
  22. \frac{a^2}{a+\sqrt{a}}