❌ 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
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.
Practice questions for Surds
Which of these is the simplified form of √48?
Explain why it is preferable to write fractions in rationalized form rather than leaving a surd in the denominator.
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