This deep dive covers Method: Rationalizing the Denominator 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 5 of 15 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Method: Rationalizing the Denominator
1
Single surd: Multiply by √a/√a
2
Example: 3/√5 = 3/√5 × √5/√5 = 3√5/5
3
Two terms: Use conjugate (a+√b) → (a-√b)
4
Example: 1/(2+√3) × (2-√3)/(2-√3) = (2-√3)/1
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