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Coursework Notes - Number


Number - Surds


[ useful expressions ][simple rationalising of surds ]


[ rationalising using diff. 2 squares ][ reduction of surds ][ rational/irrational surds]





Surds are mathematical expressions containing square roots. However, it must be emphasized that the square roots are 'irrational' i.e. they do not result in a whole number, a terminating decimal or a recurring decimal.


The rules governing surds are taken from the Laws of Indices.


rule #1


surds #1




surds  #3


rule #2


surds #2




surds #4


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Some Useful Expressions


expression #1


surds #5


expression #2 - (the difference of two squares)


surds #6


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Rationalising Surds - This is a way of modifying surd expressions so that the square root is in the numerator of a fraction and not in the denominator.


The method is to multiply the top and bottom of the fraction by the square root.


surds #7


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Rationalising expressions using the 'difference of two squares'


Remembering that : .... surds8 .....from 'useful expressions' above.


Example #1 - simplify surds #9


multiplying top and bottom by surds #10


surds #11



Example #2 - rationalise surds #12


multiply top and bottom by surds #13




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Reduction of Surds - This is a way of making the square root smaller by examining its squared factors and removing them.


surds #15



Rational and Irrational Numbers - In the test for rational and irrational numbers, if a surd has a square root in the numerator, while the denominator is '1' or some other number, then the number represented by the expression is 'irrational'.


examples of irrational surds: surds #16




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