Home >> PURE MATHS, Algebra, surds

Rules

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

Examples

Rule #2

Examples

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Some Useful Expressions

Expression #1

example

simplify        

ans.    

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Expression #2 - (the difference of two squares)

example

evaluate    

ans.

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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.

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Rationalising expressions using 'Difference of Two Squares'

Remembering that :

.....from 'useful expressions' above.

Example #1 -                                     simplify

Multiplying top and bottom by  

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Example #2 - rationalise               

Multiply top and bottom by   

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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.

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Rational and Irrational Numbers

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:

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