Key Facts

You need to know the following:
  • A square root such as is a surd. (But not, eg. )
  • Surds multiply and divide as normal:  and 
  • Surds simplify by decomposing them into a product with a square number, and applying the root to that square - eg. 

Test Yourself: Simplifying Surds

  • You can rationalise surds of the form  by multiplying by  - this keeps the fraction the same value, but 'eliminates' the surd from the bottom: 

Step-by-Step: Rationalising (simple) denominator