NumberExam Tips

Common Mistakes to Avoid

Part of Surds · GCSE GCSE Mathematics revision

This exam tips covers Common Mistakes to Avoid within Surds for GCSE Mathematics. Revise Surds in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 13 of 15 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.

Topic position

Section 13 of 15

Practice

14 questions

Recall

22 flashcards

Common Mistakes to Avoid

❌ Wrong: √a + √b = √(a+b) ✅ Right: Cannot combine different surds

√9 + √16 = 3 + 4 = 7, NOT √25 = 5

❌ Wrong: √18 = 9√2 ✅ Right: √18 = 3√2

√18 = √(9×2) = 3√2 (take square ROOT of 9)

❌ Wrong: 3√2 × 2√3 = 5√5 ✅ Right: 3√2 × 2√3 = 6√6

Multiply coefficients AND surds: 3×2=6, √2×√3=√6

❌ Wrong: Leaving denominator with surd ✅ Right: Always rationalize

1/√2 should be written as √2/2

Keep building this topic

Read this section alongside the surrounding pages in Surds. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Surds

Which of these is the simplified form of √48?

  • A. 12√2
  • B. 4√3
  • C. 3√4
  • D. 6√2
1 markfoundation

Explain why it is preferable to write fractions in rationalized form rather than leaving a surd in the denominator.

2 markshigher

Quick Recall Flashcards

What is a surd?
An irrational root that cannot be simplified to a whole number Examples: √2, √3, √5, ∛7 NOT surds: √4 = 2, √9 = 3 (these simplify to whole numbers)
What are Like Surds?
Surds with the same root part Examples of like surds: • 3√2 and 5√2 (both have √2) • 2√7 and -4√7 (both have √7) Can add/subtract like surds: 3√2 + 5√2 = 8√2

14 questions on Surds — practise free

Instant marking, adaptive difficulty, and 22 spaced repetition flashcards. Free until your GCSEs.

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