Rationalising Denominators | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Rationalising Denominators

What does it mean to rationalise a denominator?

• Fractions with surds in the denominator are not in their simplest form and require rationalization.
• Rationalizing the denominator transforms a fraction with surds in the denominator into an equivalent fraction.
  • After rationalization, the denominator becomes an integer, while any surds remain in the numerator.

How do I rationalise the denominator of a surd?

• To rationalise the denominator if the denominator is a surd
  • Step 1: Multiply the top and bottom by the surd on the denominator:
    • 
    • This ensures we are multiplying by 1; so not affecting the overall value
• Step 2: Multiply the numerator and denominators together
  •  so the denominator is no longer a surd
• Step 3: Simplify your answer if needed
• To rationalise the denominator if the denominator is an expression containing a surd:
  For example
• Step 1: Multiply the top and bottom by the expression on the denominator, but with the sign changed
  
  • This ensures we are multiplying by 1; so not affecting the overall value
  • Step 2: Multiply the expressions on the numerator and denominator together
    •  so the denominator no longer contains a surd
  • Step 3: Simplify your answer if needed