Manipulating Surds (OCR A Level Maths: Pure)

What are surds?

• If n is a positive integer and is not a square number, then √n (or any multiple of √n ) is a surd

 

• Surds are examples of irrational numbers

What do I need to know about manipulating surds?

• There are two basic rules you need to know in order to manipulate and simplify surds:

  

• When simplifying, look for square factors

• You can collect like terms with surds like you do with letters in algebra:

 

• But be careful not to confuse this with the multiplication and division rules... cannot add or subtract 'under the surd':

Where can surds be useful?

• Using surds lets you leave answers in exact form
  • e.g. rather than 
• Understanding how to simplify surds can help reduce expressions and collect like terms