Mastering Surds: Simplification to Rationalisation
This lesson covers the fundamental properties of surds, moving from basic simplification to expanding brackets and rationalising the denominator, aligned with the GCSE Higher Tier requirements.
Learning objectives
- Simplify surds by identifying the largest square factor.
- Perform operations (addition, subtraction, multiplication) with surds.
- Expand brackets involving surds and simplify the resulting expressions.
- Rationalise denominators of the form a/√b and a/(b±√c).
Lesson plan (60 minutes)
Introduction · 10 min
Starter: Retrieval practice on square numbers and simplifying basic radicals.
Direct Instruction · 10 min
Teacher-led explanation: Rules of surds and simplifying √n.
Guided Practice · 10 min
Guided practice: Multiplying surds and expanding brackets.
Independent Practice · 20 min
Differentiated task: Students work through Support, Core, or Stretch worksheets.
Assessment · 10 min
Plenary: Multiple-choice quiz to check for misconceptions.
Key vocabulary
- Irrational Number
- A number that cannot be expressed as a simple fraction; its decimal goes on forever without repeating.
- Surd
- An irrational square root of an integer.
- Radical
- The symbol √ used to indicate a root.
- Rationalising
- The process of removing a surd from the bottom of a fraction.
- Square Number
- Numbers like 1, 4, 9, 16, 25... resulting from multiplying an integer by itself.
Core worksheet (first questions)
- Simplify √200
- Simplify √45 + √80
- Simplify √12 + √300 + √3
- Expand and simplify (4 + √3)(5 + 2√3)
Quiz (sample)
1. Which of the following is equal to 2√3?
- A. √12
- B. 2√6
- C. √7
- D. 4√3
2. Simplify √50.
- A. √14
- B. 7√2
- C. 5√2
- D. 2√5
3. What is 3√3 + 5√3?
- A. 5√6
- B. 8√3
- C. 15√3
- D. √75
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