m16 Operation on Surds (1)

8/11/2019 m16 Operation on Surds (1)

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Unit 6 : Surds

Objectives:

recognise surds and state the rules

of surds,

perform arithmetical operations

(addition, subtraction, and

multiplication) on expressions

involving simple surds in the

numerator,

rationalise fractions involving surds

in the denominator,

solve problem sums involving surds,

Name : ______________ ( )

Class : ________ Date :_________


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Surd Rules

nmnm aaa

1111

nmnm aaa

1111

mnnm aa111

)(

mmm

baba

111

)(

mmm abba

111

)(

We can use the above rules to:simplify two or more surds orcombining them into one single surd


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Simplify the following surds :

24327

3:FactorCommon

mmm baab

111

)(

Example 1:

Solution:


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Simplify the following surds

28112175

7:FactorCommon

mmm baab

111

)(

Example 2:

Solution:


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271234

Example 3:

Solution:


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34327212

Example 4:

Solution:


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24348238

Simplify the following surdsExample 5:

Solution:


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22332 222 2)( bababa

Example 6:

Solution:


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22 3332

))((22

bababa

Example 7:

Solution:


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23 341132

Simplify the following surdsExample 8:

Solution:


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Rat ional ization of the Denom inator

Process of removing a surd from the denominator

Example 9:2

1

22

21

22

2

121

2

2

2

2

Multiple together!

Solution:


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Example 10:23

2

123

2

23

23

Multiple together!

Objective isto removesurds from

denominator

Conjugate Surds

Note!

22))(( bababa

Solution:


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23

23

23

2

23

2

Re-look into the question:

Multiply conjugate surds

Multiply denominatorand numerator

22))(( bababa

Example 11 :


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27

27

27

2

27

2

Rationalize the denominators:



22))(( bababa

Example 12:


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13

13

13

33

13

33




22))(( bababa

Example 13:


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324

122




22))(( bababa

Example 14:


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32233223

32233223

3223

3223




22))(( bababa

mmm abba

111

)(

Example 15:


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3253

5237




22))(( bababa

Example 16:


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73

1

73

1


Determine the LCM


7373

Example 17:


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22 )53(

53

)35(

53

2222 )5(532)3(53

)3(352)5(53


Expand thedenominators

Find the LCM 1541542

Example 18:


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524

23

524

235


Same denominator

Rationalization

Example 19:


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Example 20: Given that k = , evaluate35

35

2

2 1

kk


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Surds Check list

Complete Skill Check 1

Complete Skill Check 2

Complete Exercise 2.1 (textbook)

Complete Unit 6 Assignment 1


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