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
    A rectangle has length (3+5)(3 + \sqrt{5}) cm and width (3−5)(3 - \sqrt{5}) cm.(3 + √5) cm(3 − √5) cmDiagram NOT accurately drawn

    (a) Work out the area of the rectangle, in cm².

    (b) Work out the perimeter of the rectangle, in cm.
    Level 5 · 4 marksTry it