Surds — GCSE Mathematics Revision
Revise Surds for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP.
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Next step: Rounding & Estimation
Continue in the same course — structured practice and explanations on StudyVector.
Go to Rounding & EstimationWhat is Surds?
A surd is an irrational root that cannot be simplified to a whole number, like √2 or √5. Simplify surds by finding the largest square factor: √12 = √(4×3) = 2√3. You can add and subtract like surds (2√3 + 5√3 = 7√3) but not unlike surds. Rationalise the denominator by multiplying top and bottom by the surd: 1/√3 = √3/3.
Step-by-step explanationWorked examples
Worked example 1: Core method
Simplify √50 + √8. √50 = √(25×2) = 5√2. √8 = √(4×2) = 2√2. So √50 + √8 = 7√2.
Worked example 2: Exam variation
Now change one detail in the question and keep the same structure: name the Surds idea being tested, show the method or evidence, then explain why it answers the command word. This helps GCSE Mathematics students avoid memorising one surface pattern.
Worked example 3: Mark-scheme check
Finish by checking the answer against marks: one point for the correct Surds idea, one for accurate working or evidence, and one for a precise final statement. If any step is vague, rewrite it before moving to timed practice.
Mini lesson for Surds
1. Understand the core idea
A surd is an irrational root that cannot be simplified to a whole number, like √2 or √5. Simplify surds by finding the largest square factor: √12 = √(4×3) = 2√3.
Can you explain Surds without copying the notes?
2. Turn it into marks
Simplify √50 + √8. √50 = √(25×2) = 5√2.
Underline the method, evidence, or command-word move that would earn credit in GCSE Number.
3. Fix the likely mark leak
Watch for this mistake: Trying to add unlike surds: √2 + √3 ≠ √5.
Write one correction rule before doing another practice question.
Practise this topic
Jump into adaptive, exam-style questions for Surds. Free to start; sign in to save progress.
Mini quiz: Surds
Three quick checks for revision practice. They are original StudyVector prompts, not official exam-board questions.
Question 1
In one GCSE sentence, explain what Surds is testing.
Answer: A surd is an irrational root that cannot be simplified to a whole number, like √2 or √5. Simplify surds by finding the largest square factor: √12 = √(4×3) = 2√3.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Surds question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Trying to add unlike surds: √2 + √3 ≠ √5." What should their next repair task be?
Answer: Do one Surds question and review the mistake type.
Mark focus: Error correction and next-step practice.
Surds flashcards
Core idea
What is the main idea in Surds?
A surd is an irrational root that cannot be simplified to a whole number, like √2 or √5. Simplify surds by finding the largest square factor: √12 = √(4×3) = 2√3.
Common mistake
What mistake should you avoid in Surds?
Trying to add unlike surds: √2 + √3 ≠ √5.
Practice
What is one useful practice task for Surds?
Answer one Surds question and review the mistake type.
Exam board
How should you use board notes for Surds?
Use your own GCSE specification for exact paper wording and depth.
Common mistakes
- 1Trying to add unlike surds: √2 + √3 ≠ √5.
- 2Not fully simplifying — √18 should become 3√2, not left as √18 or simplified only to √(9×2).
- 3Forgetting to rationalise the denominator when the question requires an exact answer.
- 4Errors when expanding (a + √b)(a - √b) — this is the difference of two squares pattern.
Surds exam questions
Exam-style questions for Surds with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Surds
Core concept
A surd is an irrational root that cannot be simplified to a whole number, like √2 or √5. Simplify surds by finding the largest square factor: √12 = √(4×3) = 2√3. You can add and subtract like surds (2…
Frequently asked questions
What does rationalise the denominator mean?
It means rewriting a fraction so there is no surd in the denominator. Multiply the top and bottom by the surd (or by the conjugate if the denominator is a + √b).
Are surds on the Foundation tier?
Basic surd simplification appears on some Foundation papers, but most surd work (rationalising, expanding) is Higher tier only.