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.

Start practising Read the lesson

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

DifficultyAll Level 3 Level 4 Level 5

1
Rationalise the denominator of $\dfrac{5 + \sqrt{2}}{\sqrt{2}}$ . Simplify your answer.
Level 4 · 2 marksTry it
2
Rationalise the denominator of $\dfrac{4}{3 + \sqrt{5}}$ . Give your answer in its simplest form.
Level 4 · 3 marksTry it
3
Rationalise the denominator of $\dfrac{3 + \sqrt{6}}{\sqrt{3}}$ . Simplify your answer.
Level 4 · 3 marksTry it
4
Rationalise the denominator of $\dfrac{6}{\sqrt{7} - 1}$ . Give your answer in its simplest form.
Level 4 · 3 marksTry it
5
Rationalise the denominator of $\dfrac{14}{3 - \sqrt{2}}$

Give your answer in the form $a + b\sqrt{2}$ , where $a$ and $b$ are integers. (3 marks)
Level 4 · 3 marksTry it

1 more question on rationalising the denominator

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free