This deep dive covers Higher Level: Complex Rationalization 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 12 of 14 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 12 of 14
Practice
14 questions
Recall
22 flashcards
Higher Level: Complex Rationalization
For denominators with two terms, use the conjugate:
- Conjugate of (a + √b): (a - √b)
- Why it works: (a+√b)(a-√b) = a² - b (no surd!)
Example: Rationalize 1/(3 + √7)
Multiply by (3 - √7)/(3 - √7):
= (3 - √7)/[(3 + √7)(3 - √7)]
= (3 - √7)/(9 - 7)
= (3 - √7)/2