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WEEK THREE
SURDS
CONTENTS
SUB TOPIC: DEFINITION OF SURDS
Certain numbers can be expressed as ratios of two integers, i. e . Where p and q belong to the set of integers and q ≠ 0, such numbers are called rational numbers.
Examples of rational numbers are; 3, 11/2, 3.5, -7.1 etc. Each of them can be expressed in the form , where p and q are integers such that q ≠ 0 as follows:
Some numbers however, cannot be expressed as ratios of two integers, i.e p/q such that q ≠ 0, p and q belonging to the set of integers. Examples of such numbers are , , etc such numbers are said to be irrational. Other examples of irrational numbers are pi( )and the number exponential ( ). Their exact values cannot be determined. Their approximate values can only be determined.
and 2.7183.
SURDS are irrational numbers which are roots of rational numbers. Examples of surds are , etc.
We shall consider only expressions which contains one or more square roots of prime numbers of their multiples. Such expressions are called quadratic surds.
CLASS ACTIVITIES:
SUB TOPIC: RULES OF MANIPULATING SURDS
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