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**www.maths4scotland.co.uk**Higher Mathematics Surds Next**Surds**Higher Mathematics What are Surds A surd is a square root which cannot be evaluated without approximation.**Surds**Higher Mathematics What are Surds A surd is an irrational number An irrational number cannot be written as a simple fraction i.e. as It is a non-recurring decimal**Surds**Higher Mathematics Why are surds of interest A surd is a square root which cannot be evaluated without approximation. These often occur when using Pythagoras’ Theorem Trigonometry Using surds allows us to be EXACT**Surds**Higher Mathematics Examples of Surds etc. A good rule of thumb is to think of a surd as: Any root that cannot be evaluated as a whole number. For example: is not a surd**Surds**Higher Mathematics Which of these are surds ? Yes Yes No Yes No**Surds**Higher Mathematics Rules of surds We can add or subtract surds if they are the same. Just like algebra:**Surds**Higher Mathematics Examples Simplify**Surds**Higher Mathematics Rules of surds We can multiply surds Let’s check this out with simple numbers**Surds**Higher Mathematics Rules of surds We can multiply surds in general Note that this works both ways**Surds**Higher Mathematics WARNING Let’s check this out with simple numbers**Surds**Higher Mathematics Examples Simplify**Surds**Higher Mathematics Rules of surds We can divide surds Let’s check this out with simple numbers**Surds**Higher Mathematics Rules of surds We can divide surds in general Note that this works both ways**Surds**Higher Mathematics A useful tip**Surds**Higher Mathematics Examples Simplify**Surds**Higher Mathematics Rules**Surds**Higher Mathematics Applications We can use the rules of surds for simplification Simplify: Look for largest square factor**Surds**Higher Mathematics Applications We can use the rules of surds for simplification Simplify: Look for largest square factor**Surds**Higher Mathematics Applications We can use the rules of surds for simplification Simplify: Look for largest square factor**Surds**Higher Mathematics Applications We can use the rules of surds for simplification Simplify: Look for largest square factor**Surds**Higher Mathematics Applications We can use the rules of surds for simplification Simplify:**Surds**Higher Mathematics Applications We can use the rules of surds for simplification Simplify: Use FOIL**Surds**Higher Mathematics Applications We can use the rules of surds for simplification Simplify: Use FOIL**Surds**Higher Mathematics Applications Rationalise the denominator and simplify where possible: To get rid the surd – multiply top and bottom by the surd**Surds**Higher Mathematics Applications Rationalise the denominator and simplify where possible: To get rid the surd – multiply top and bottom by the surd**Surds**Higher Mathematics Applications Rationalise the denominator and simplify where possible: To get rid the surd – multiply top and bottom by the conjugate conjugate - the same expression with the opposite sign in the middle**Surds**Higher Mathematics Applications Rationalise the denominator and simplify where possible: To get rid the surd – multiply top and bottom by the conjugate conjugate - the same expression with the opposite sign in the middle**C**P D www.maths4scotland.co.uk © CPD 2004 Quit