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MathidiaMathematics Academy
Surds, indices and exact algebra
Lesson 6 of 75
Introduction

Expanding surd brackets

Objective. Expand and simplify products involving two surds.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Expanding surd brackets is developed here as connected GCSE mathematics, not a memorised shortcut. Preserve exact values through sophisticated algebraic manipulation. The lesson moves from a precise representation and key definitions to fluent procedure, linked reasoning and an unfamiliar application. Learners compare possible methods, state restrictions and assumptions, preserve exact values where appropriate, and justify accuracy, notation and units before evaluating whether the result is mathematically and contextually reasonable.

Worked example

Work out 5² × 5⁻¹.

Work out 5² × 5⁻¹
Illustrated card showing Work out 5² × 5⁻¹
  1. 1Translate the information into a labelled diagram, table, graph or algebraic statement and identify every constraint.
  2. 2Select the most efficient GCSE method, explain why its conditions apply, and keep exact values until approximation is requested.
  3. 3Carry out each transformation on a separate justified line, tracking signs, units, domains and required accuracy.
  4. 4Verify with substitution, an inverse method, estimation or a second representation. The checked result is 5.

Answer: 5

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

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Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

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Common mistake. A common error in expanding surd brackets is applying a familiar rule before checking its conditions, domain or direction. Name the structure first, retain exact values, and test the final result against every original constraint.

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