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
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 15 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
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.