Edexcel International AS Maths: Pure 1

Revision Notes

1.1.2 Manipulating Surds

Test Yourself

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

Surd and not surd, A Level & AS Level Pure Maths Revision Notes 

  • 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:

 List of surd laws2, A Level & AS Level Pure Maths Revision Notes 

  • When simplifying, look for square factors

2-1-2-surds-simplify

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

2.1.2 Surds collect like terms, Edexcel A Level Maths: Pure revision notes

 

  • But be careful not to confuse this with the multiplication and division rules... cannot add or subtract 'under the surd':Surds add subtract warning, A Level & AS Level Pure Maths Revision Notes

Where can surds be useful?

  • Using surds lets you leave answers in exact form
    • e.g. 5 square root of 2 rather than 7.071067812
  • Understanding how to simplify surds can help reduce expressions and collect like terms

    2-1-2-surds-collect

Exam Tip

  • 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

Manipulating Surds Example1, A Level & AS Level Pure Maths Revision Notes

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Roger

Author: Roger

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.