Rationalising the Denominator with Surds (Edexcel IAL Maths)

Surds - Rationalising the Denominator

Spec point — 1.2

Rationalising the denominator with surds

How do I rationalise the denominator?

• Rationalising a denominator changes a fraction with surds in its denominator, into an equivalent fraction where the denominator is a rational number (usually an integer) and any surds are in the numerator

• There are three cases you need to know how to deal with when rationalising denominators:

Exam Hint

• If an exam question asks you to give an answer, for example, "in the form p + q√3 , where p and q are rational numbers", this does NOT mean that p and q have to be integers, or positive!
• Remember: both integers and fractions (both positive and negative) are rational numbers

Worked Example