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MathematicsYear 11en

📐 Surds: Simplifying and Rationalising Denominators

Master the techniques for simplifying surd expressions and eliminating surds from denominators in algebraic fractions. **What you'll learn:** - Simplify surd expressions by factoring perfect squares - Identify and combine like surds - Rationalise denominators using conjugate pairs - Simplify complex surd fractions with multiple terms

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Questions in this quiz

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  1. Question 1

    Simplify 50\sqrt{50}.

  2. Question 2

    Combine the like surds: 37+273\sqrt{7} + 2\sqrt{7}.

  3. Question 3

    Simplify 72\sqrt{72} to the form aba\sqrt{b} where a=a = ___ and b=b = ___.

  4. Question 4

    12+27=39\sqrt{12} + \sqrt{27} = \sqrt{39}.

  5. Question 5

    Rationalise the denominator: 15\frac{1}{\sqrt{5}}.

  6. Question 6

    Rationalise the denominator: 38\frac{3}{\sqrt{8}}.

  7. Question 7

    Rationalise the denominator: 42−3\frac{4}{2 - \sqrt{3}}.

  8. Question 8

    Simplify 18+82\frac{\sqrt{18} + \sqrt{8}}{\sqrt{2}}.

  9. Question 9

    Simplify 18+82\frac{\sqrt{18} + \sqrt{8}}{\sqrt{2}}.

  10. Question 10

    Rationalise and simplify: 33+1\frac{\sqrt{3}}{\sqrt{3} + 1}.