GCSE · Surds

Expanding brackets with surdsExam-style questions

Why surds multiply out exactly like algebra — with √a·√a collapsing to a — how squares like (4 − √2)² keep their middle term, and why conjugate pairs multiply to a whole number.

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

DifficultyAllLevel 3Level 4Level 5
  1. 1
    Expand and simplify 3 (4+3)\sqrt{3}\,(4 + \sqrt{3}).
    Level 3 · 2 marksTry it
  2. 2
    Expand and simplify 5 (5−2)\sqrt{5}\,(\sqrt{5} - 2).
    Level 3 · 2 marksTry it
  3. 3
    Expand and simplify (3+2)(3−2)(3 + \sqrt{2})(3 - \sqrt{2}).
    Level 3 · 2 marksTry it
  4. 4
    Expand and simplify (2+5)(3−5)(2 + \sqrt{5})(3 - \sqrt{5}).
    Level 4 · 3 marksTry it
  5. 5
    Write (4−2)2(4 - \sqrt{2})^2 in the form a+b2a + b\sqrt{2}, where aa and bb are integers.
    Level 4 · 2 marksTry it

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