# IGCSE Surds Dr J Frost ([email protected]) Objectives: (from IGCSE Surds Dr J Frost ([email protected]) Objectives: (from the specification) Last modified: 22nd August 2015 RECAP :: Surds Simplify the following: ? ? ? ? NEW! :: Rationalising More Complex Denominators Youre already used to rationalising a denominator, the idea being that we dont like to divide things by an irrational number. ? ? But what do we multiply the top and bottom by if we have a more complicated denominator?

? ? We basically do the same but with the sign reversed (this is known as the conjugate). That way, we obtain the difference of two squares. Since , any surds will be squared and thus well end up with no surds in the denominator. More Examples 3 6 +2 3 6+ 6 = ? ? 2 6 2 6 +2 You can explicitly expand out in the denominator, but remember that so we get Just remember: difference of

two squares! 3 2+4 + + + + ? ? = 5 27 + Test Your Understanding Jan 2013 Paper 1 Write in the form where is an integer. Rationalise the denominator and simplify ?

June 2013 Paper 1 Solve Give your answer in the form where and are integers. ? + = + ? + Exercises 1 [June 2012 Paper 1 Write this ration in its simplest form: ? 3

Expand and simplify: ? 4 Rationalise the denominator, giving your answer in the form . 2 Rationalise the denominator and simplify the following: a b c d ? ? Solve giving your answer in the form .

5 Solve ? ? ? Simplify: 6 ? ? 7 e ? ?