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
Simplify fully $\sqrt{200} + \sqrt{18} - \sqrt{50}$ .
Level 4 · 3 marksTry it
2
Simplify fully $3\sqrt{8} - \sqrt{18} + \sqrt{2}$ .
Level 4 · 3 marksTry it
3
(a) Write $\sqrt{180}$ in the form $a\sqrt{5}$ , where $a$ is an integer.

(b) Hence, or otherwise, work out $\dfrac{\sqrt{180}}{\sqrt{5}}$ .
Level 4 · 3 marksTry it