SS1 First Term Further Mathematics Lesson Note – Surds

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WEEK THREE

SURDS

CONTENTS

1. Definition of Surds
2. Rules for manipulating surds
3. Rationalization of the denominator.
4. Equality of surds.
5. Equations in irrational forms

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:

• 3 = (b) 1¹/₂ =  (c) 3.5 = 3¹/₂ =  (d) -7.1 =

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:

1. What is a surd?
2. Write out the examples of surd
3. Differentiate between rational and irrational numbers.

SUB TOPIC: RULES OF MANIPULATING SURDS

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