GCSE · Surds

Rationalising the denominatorExam-style questions

Why multiplying top and bottom by the same thing changes nothing, how √a in a denominator is cleared by √a, and how a conjugate clears a two-term denominator like 3 + √5.

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16 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 3Level 4Level 5
  1. 1
    Rationalise the denominator of 63\dfrac{6}{\sqrt{3}}. Give your answer in its simplest form.
    Level 3 · 2 marksTry it
  2. 2
    Rationalise the denominator of 105\dfrac{10}{\sqrt{5}}. Give your answer in its simplest form.
    Level 3 · 2 marksTry it
  3. 3
    (a) Rationalise the denominator of 123\dfrac{12}{\sqrt{3}} Give your answer in its simplest form. (2 marks)

    (b) Expand and simplify (5+2)(5−2)(\sqrt{5} + 2)(\sqrt{5} - 2) (2 marks)
    Level 3 · 4 marksTry it
  4. 4
    Rationalise the denominator of 5+22\dfrac{5 + \sqrt{2}}{\sqrt{2}}. Simplify your answer.
    Level 4 · 2 marksTry it
  5. 5
    Rationalise the denominator of 43+5\dfrac{4}{3 + \sqrt{5}}. Give your answer in its simplest form.
    Level 4 · 3 marksTry it

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