GCSE · Surds

Simplifying surdsExam-style questions

Why surds are kept as exact values, why √(ab) = √a × √b lets you pull square factors out, and how to collect like surds — and why √a + √b is not √(a+b).

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

DifficultyAll Level 3 Level 4 Level 5

1
Write $\sqrt{48}$ in the form $a\sqrt{b}$ , where $a$ and $b$ are integers and $b$ is as small as possible.
Level 3 · 2 marksTry it
2
Simplify fully $5\sqrt{12} - 2\sqrt{27}$ .
Level 3 · 3 marksTry it
3
Work out $\sqrt{8} \times \sqrt{18}$ . Give your answer as an integer.
Level 3 · 2 marksTry it
4
Write $\sqrt{72}$ in the form $a\sqrt{b}$ , where $a$ and $b$ are integers and $b$ is as small as possible.
Level 3 · 2 marksTry it
5
Simplify fully $\sqrt{32} + \sqrt{50}$ .
Level 3 · 2 marksTry it

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