Integrated Mathematics Surds. Irrational Number Number that cannot be expressed as a fraction of two...
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![Page 1: Integrated Mathematics Surds. Irrational Number Number that cannot be expressed as a fraction of two integers.](https://reader035.fdocuments.in/reader035/viewer/2022081504/5697bfd01a28abf838caa5c8/html5/thumbnails/1.jpg)
Integrated Mathematics
Surds
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Irrational Number•Number that cannot be expressed as a fraction of two integers
2 6
2
1
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27
1
2
3 27
1
Think!Which of the following is NOT a irrational number?
26
36
1
25
1
55
9
1)3
1( 2 x x
x
Irrational number
Irrational number
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Rules of Indices and Surds 1mma a
mmm baba111
)(
m m ma b ab
m
mm
a a
bb
mmm abba111
)(
a a a 1 1
2 2a a a
a b a b a b a b
![Page 5: Integrated Mathematics Surds. Irrational Number Number that cannot be expressed as a fraction of two integers.](https://reader035.fdocuments.in/reader035/viewer/2022081504/5697bfd01a28abf838caa5c8/html5/thumbnails/5.jpg)
Simplify
24327
9 3 81 3
3933
38139
312
m m mab a b
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Simplify
28112175
25 7 16 7 4 7
727475
74716725
77
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Simplify
271234
933434
3)24(3
3
38
333234
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Simplify
22332
30 12 6
)2)(9(632234
1861212
222 2)( bababa 23 32 2332 32 23
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Simplify
223332
33325
3215
)132(5
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Rationalization of the Denominator
•Process of removing a surd from the denominator
•Example:2
1
2
2
2
1
22
2
12
1
2
2
2
2
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•Example:23
2
23
23
23
2
2323
232
123
2
22
23
232
23
23
Multiple together!
1
432
43
232
432
Objective is to remove surds from
denominator
Conjugate Surds
Note!
22))(( bababa
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23
23
23
2
23
2
Re-look into the question:
2323
232
Multiply conjugate surds
Multiply denominator and
numerator
22))(( bababa
22
23
232
3241
432
![Page 13: Integrated Mathematics Surds. Irrational Number Number that cannot be expressed as a fraction of two integers.](https://reader035.fdocuments.in/reader035/viewer/2022081504/5697bfd01a28abf838caa5c8/html5/thumbnails/13.jpg)
27
27
27
2
27
2
Rationalize the denominators:
2727
272
Multiply conjugate surds
Multiply denominator and
numerator
22))(( bababa
22
27
272
47
272
3
272
![Page 14: Integrated Mathematics Surds. Irrational Number Number that cannot be expressed as a fraction of two integers.](https://reader035.fdocuments.in/reader035/viewer/2022081504/5697bfd01a28abf838caa5c8/html5/thumbnails/14.jpg)
13
13
13
33
13
33
Rationalize the denominators:
1313
1333
Multiply conjugate surds
Multiply denominator and
numerator
22))(( bababa
22
2
13
33333
13
3323
32
32
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23
21019
932
3242616
324
324122
324
324
324
122
324
324
324
122
22
324
122
Rationalize the denominators:
Multiply conjugate surds
Multiply denominator and
numerator
22))(( bababa
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3223
3223
3223
3223
3223
3223
Rationalize the denominators:
32233223
32233223
Multiply conjugate surds
Multiply denominator and
numerator
22))(( bababa
22
2
3223
3223
22
22
3223
323223223
6256
61230
3429
3461229
mmm abba111
)(
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3253
5237
Rationalize the denominators:
Multiply conjugate surds
Multiply denominator and
numerator
22))(( bababa
33
721525
1245
15430421521
32533253
32535237
3253
3253
3253
5237
![Page 18: Integrated Mathematics Surds. Irrational Number Number that cannot be expressed as a fraction of two integers.](https://reader035.fdocuments.in/reader035/viewer/2022081504/5697bfd01a28abf838caa5c8/html5/thumbnails/18.jpg)
73
1
73
1
Rationalize the denominators:
Determine the LCM
Multiply denominator and
numerator
73
1
73
1
73
73
7373
73
7373
73
73
73
7373
7373
7373
2
3
4
32
73
32
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)154(2
53
)154(2
53
22 )53(
53
)35(
53
2222 )5(532)3(
53
)3(352)5(
53
Rationalize the denominators:
Expand the denominators
51523
53
31525
53
1528
53
1528
53
Find the LCM
)154(
)154(
)154(2
53
)154(
)154(
)154(2
53
)1516(2
)755415312()755415312(
)1(2
)7512(2 3512
1541542
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524
23235
524
23
524
235
Rationalize the denominators:
Same denominator
Rationalization
2016
1042851632
524
228
)524)(524(
)524)(228(
10225484
1042851632
524
524