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Grade 11 · Exponents and Surds
Surds: Simplifying & Rationalising (Grade 11)
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  / 34

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    Simplify √72
    (2)
  2. 2
    Simplify √50
    (2)
  3. 3
    Simplify √98
    (2)
  4. 4
    Simplify √12 + √27
    (2)
  5. 5
    Simplify 3√2 + √50
    (2)
  6. 6
    Simplify √5 × √20
    (2)
  7. 7
    Expand (√3 + 2)(√3 − 5)
    (3)
  8. 8
    Rationalise 6/(√3)
    (2)
  9. 9
    Rationalise 1/(√5)
    (2)
  10. 10
    Rationalise 4/(1 + √2)
    (3)
  11. 11
    Solve for x: √(x − 4) = 5
    (3)
  12. 12
    Solve for x: 2√x + 1 = 9
    (3)
  13. 13
    Solve for x: √(x + 6) = x, and reject any invalid answer with a reason.
    (4)
  14. 14
    Explain why √(x + 1) = −3 has no solution.
    (2)
TOTAL: 34 marks
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