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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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Simplify the following surds
271234
Example 3:
Solution:
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Simplify the following surds
34327212
Example 4:
Solution:
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24348238
Simplify the following surdsExample 5:
Solution:
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Simplify the following surds
22332 222 2)( bababa
Example 6:
Solution:
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Simplify the following surds
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:
Multiply conjugate surds
Multiply denominatorand numerator
22))(( bababa
Example 12:
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13
13
13
33
13
33
Rationalize the denominators:
Multiply conjugate surds
Multiply denominatorand numerator
22))(( bababa
Example 13:
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324
122
Rationalize the denominators:
Multiply conjugate surds
Multiply denominatorand numerator
22))(( bababa
Example 14:
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32233223
32233223
3223
3223
Rationalize the denominators:
Multiply conjugate surds
Multiply denominatorand numerator
22))(( bababa
mmm abba
111
)(
Example 15:
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3253
5237
Rationalize the denominators:
Multiply conjugate surds
Multiply denominatorand numerator
22))(( bababa
Example 16:
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73
1
73
1
Rationalize the denominators:
Determine the LCM
Multiply denominatorand numerator
7373
Example 17:
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22 )53(
53
)35(
53
2222 )5(532)3(53
)3(352)5(53
Rationalize the denominators:
Expand thedenominators
Find the LCM 1541542
Example 18:
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524
23
524
235
Rationalize the denominators:
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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