Manipulating Surds (Edexcel IAL Maths)

Spec point — 1.2

Manipulating surds

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. $5\sqrt{2}$ rather than $7.071067812$

• Understanding how to simplify surds can help reduce expressions and collect like terms

Exam Hint

• Leaving answers in surd form can be really helpful when you need to carry an exact value through to another part of working
• When simplifying surds, remembering your square numbers is really helpful!

Worked Example