EXPRESIONES ALGEBRAICAS IRRACIONALES

1. Asignatura:
Matemática II
MAT 113
Unidad II
Expresiones Algebraicas Irracionales
Actividad No.2
Practica Individual
Participante:
Matricula:
Facilitador/a: Margarita Franco M.A.
Bibliografía: Algebra y Trigonometría, Dennis –Z-Gill

2. Matemática II
MAT 113
Práctica unidadII:ExpresionesIrracionales
Simplifiquelassiguientesexpresionesirracionales.
ba2
50 = √ 2.52 𝑎2 𝑏 = 5a√ 2 b
432234
912884 babbabaa  =
√22 𝑎2. 𝑎2 + 22.2 𝑎2. 𝑎. 𝑏 − 22.2 𝑎2 𝑏2−.22. 2 𝑎 𝑏2 𝑏1 + 32 𝑏2. 𝑏2
=2𝑎2+2ª-2ab-2b-2b+3𝑏2
√2𝑎𝑏 − 2 − 2𝑎𝑏
=4ª+2ª-2ab-2b+3𝑏2
√2𝑎𝑏 − 2 − 2𝑎𝑏
=6𝑎2 − 2𝑎𝑏 − 2𝑏 + 3𝑏2
√2𝑎𝑏 − 2 − 2𝑎𝑏
973
442 cbaa =2a √𝟐. 𝟐𝟐 𝒂 𝟑 𝒃 𝟕 𝒄 𝟗 =2a √2.2.11 𝑎3 𝑏7 𝑐9 =2a=√22.11 𝑎3 𝑏7 𝑐9 = 2𝑎. 2√11 𝑎3 𝑏7 𝑐9 =
=4a.a √11. 𝑎2. 𝑎 𝑏6 . 𝑏 𝑐8. 𝑐 = 4a. 𝑎. 𝑏3.𝑐4
√11. 𝑎. 𝑏. 𝑐
=4 𝑎2 𝑏3 𝑐4.√11𝑎𝑏𝑐
442
168 xyyx  =√22. 2 𝑥2 𝑦4 + 24 𝑥 𝑦4= 2x𝑦2 + 22 𝑦2
√2𝑥
=2x𝑦2 + 4𝑦2
√2𝑥
aaa 36369 23
 =√9𝑎(𝑎2 − 4𝑎 + 4 =√9𝑎(𝑎 − 2)2 = (3a−6)√ 𝑎
3
42
2
16
27
3
2
ba
x
=
2
3
√33 𝑥227𝑥13
√(2)(8) 𝑎2 𝑏3 𝑏
3 =
2
3
√
33 𝑥2
(2)(23) 𝑎2 𝑏3 𝑏
3
=
(2)(3)
3(2)( 𝑏)
√
𝑥2
2𝑎2 𝑏
3
=
1
𝑏
√
𝑥2
2𝑎2 𝑏
3
=
√𝑥23
𝑏 √2𝑎2 𝑏
3 =(
√𝑥23
𝑏 √2𝑎2 𝑏
3 ) =[
√(2𝑎2 𝑏)23
√(2𝑎2 𝑏)23 ]
=
√(𝑥2)(2𝑎2 𝑏)23
𝑏 √(2𝑎2 𝑏)33 =
√(𝑥2)(2𝑎2 𝑏)23
𝑏(2𝑎2 𝑏)
=
√( 𝑥2)(4𝑎4 𝑏2)
3
2𝑎2 𝑏2
=
√( 𝑥2)(4𝑎3 𝑎 𝑏2)
3
2𝑎2 𝑏2
=
√( 𝑥)(4𝑎 𝑏2)
3
2𝑎2 𝑏2
=
√( 𝑥)(4𝑎 𝑏2)
3
2𝑎𝑏2
=
√4𝑎 𝑏2 𝑥23
2𝑎 𝑏2
4
3
2
4
81
2
yx
a
xy
=
2𝑥𝑦 √81𝑎24
√4𝑥3 𝑦
4 =
2𝑥𝑦 √34 𝑎24
√4𝑥3 𝑦
4 =
(2𝑥𝑦)(3) √𝑎24
√4𝑥3 𝑦
4 =
6𝑥𝑦 √𝑎24
√4𝑥3 𝑦
4 =
(
6𝑥𝑦 √𝑎24
√4𝑥3 𝑦
4 ) =[
√ (4𝑥3 𝑦)34
√ (4𝑥3 𝑦)34 ] =
6𝑥𝑦 √𝑎2(4𝑥3 𝑦)34
√(4𝑥3 𝑦)
4
(4𝑥3 𝑦)3
=
6𝑥𝑦 √𝑎2(4𝑥3 𝑦)34
√(4𝑥3 𝑦)44 =
6𝑥𝑦 √𝑎2(4𝑥3 𝑦)34
4𝑥3 𝑦
=
3 √𝑎2(4𝑥3 𝑦)34
2𝑥2
=
3 √𝑎243 𝑥9 𝑦34
2𝑥2
=

3. 3 √𝑎2(22)3 𝑥8 𝑥 𝑦34
2𝑥2
=
3 √𝑎2(26)𝑥8 𝑥 𝑦34
2𝑥2
=
3 √𝑎2(24)(22)𝑥8 𝑥 𝑦34
2𝑥2
=
3 (2)𝑥2 √𝑎2(22)𝑥 𝑦34
2𝑥2
=3 (2)𝑥2√𝑎2(22)𝑥 𝑦34
=3√4𝑎2 𝑥 𝑦34
10 1510
32 yx = √25 𝑥1010
𝑦10 𝑦5=𝑥𝑦 √2510
𝑦5
))(( 22
baba  =√( 𝑎 − 𝑏)( 𝑎 + 𝑏)(𝑎 − 𝑏) = √(𝑎 − 𝑏)2(𝑎 + 𝑏) =( 𝑎 − 𝑏)√( 𝑎 + 𝑏)
3 82
1282 yxxy =2x𝑦3=√24.23 𝑥2 𝑦4 =2x𝑦3. 22 𝑥 𝑦2√23 =42 𝑥 𝑦5
En lossiguientesproblemas racionalice el denominador.
ba 
1
=
1(√ 𝑎 +√ 𝑏 )
(√ 𝑎−𝑏 )(√ 𝑎+𝑏 )
=
(√ 𝑎 +√ 𝑏 )
𝑎−𝑏
3
2
1
ab =
1
√23
√ 𝑎𝑏3 =
22
3⁄ ( 𝑎𝑏)2
3⁄
2𝑎𝑏
= 2 2
3⁄ ( 𝑎𝑏) 2
3⁄
1
1
x =
1(√ 𝑥−1)
(√𝑥+1 )(√ 𝑥−1)
=
1√ 𝑥−1
√𝑥2−12
=
√ 𝑥−1
𝑥−1
3
2
5
t =
5(√ 𝑡−2)2
3⁄
√𝑡−2 )(√ 𝑡−2)2
3⁄
=
5(√ 𝑡−2)2
3⁄
𝑡−2
yx
yx


=
(√ 𝑥+√ 𝑦)(√ 𝑥+√ 𝑦)
(√ 𝑥−√ 𝑦)(√ 𝑥+√ 𝑦)
=
(√ 𝑥+𝑦)2
𝑥−𝑦
Realizalassiguientesoperaciones conexpresionesalgebraicasirracionales.
22
5254 xx  = 2√5𝑥2
yzyz 443  =4√4𝑦𝑧
xx 8*5 =√5 𝑥 .8𝑥 = √40𝑥
5
25
=√25 / √5 = √5 /√1 = √5
23
522 yx 
=2.√2𝑥3 + √5𝑦2

4. = 2.√2.√𝑥3 + √5 . √𝑦2 = 4√𝑥3+ 10√ 𝑦 = 14√𝑥3 𝑦
5452  =6√5
22
94925 axbax 
=√25𝑎𝑥2 =5x√ 𝑎
=√49𝑏 =7√ 𝑏
=√9𝑎𝑥2 =3𝑥√ 𝑎
= (5x-3x) √ 𝑎+ 7√ 𝑏
= 2𝑥√ 𝑎 + 7√ 𝑏
2222
41692 mnmnnmnm 
=2.√𝑚2 𝑛 =2m√ 𝑛
=√9𝑚2 𝑛 =3m√ 𝑛
=√16𝑚 𝑛2 =4n√ 𝑚
=√4𝑚 𝑛2 =2n√ 𝑚
=2m√ 𝑛-3m√ 𝑛+4n√ 𝑚-2n
= (2m-3m) √ 𝑛+ (4n-2n) √ 𝑚
=m√ 𝑛+2√ 𝑚
33 2
38*9
4
3
aba
=√9.3𝑎23
𝑎𝑏 =6 √32. 3𝑎3.3𝑎𝑏
3
= 6 √33. 𝑎3 𝑏
3
6.3.a √ 𝑏3
= 18a √ 𝑏3
4 33 22
32* baba =2.√𝑎2 𝑏23
* √3𝑎34
𝑏
= 2 √𝑎2 𝑏212
12/3 ∗ √3𝑎3 𝑏
12
12/4
=2 √(𝑎2 𝑏2)412
∗ √(3𝑎3 𝑏)312
= 2 √𝑎8 𝑏812
∗ √33 𝑎9 𝑏312
=2 √𝑎8 𝑏833 𝑎9 𝑏312
=2 √2𝑎17 𝑏1112
=2 √27𝑎12 𝑎5 𝑏1112
=2a √27𝑎5 𝑏1112
5 43 2
16
4
3
*4
3
2
nmm
=
6
12
√4𝑚24
√16𝑚4 𝑛
5
=
1
2
√4𝑚24
√16𝑚4 𝑛
5
=
1
2
√(4𝑚2)15 15
3
√(16𝑚4 𝑛5
)
15
3
=
1
2
√(4𝑚2)515
√(16𝑚4 𝑛)315
=
1
2
√45 𝑚1015
√163 𝑚12 𝑛315
=
1
2
√[(2)(2)]5 𝑚1015
√[(2)(2)(2)(2)]5 𝑚12 𝑛315
=
1
2
√210 𝑚1015
√212 𝑚12 𝑛315
=
1
2
√210 𝑚10212 𝑚12 𝑛315
=
1
2
√222 𝑚22 𝑛315
=

5. 1
2
√21527 𝑚15 𝑛315
=
1
2
(𝑚) √27 𝑚7 𝑛315
= 𝑚 √27 𝑚7 𝑛315
= 𝑚 √128𝑚7 𝑛315
a
a
ax 5
1
*2
=√2 √ 𝑎 𝑥
1
𝑎
√5𝑎 =√2 √5 √ 𝑎 √ 𝑎 𝑥
1
𝑎
=√2 √5 𝑥
1
𝑎
=
(1x√2 √5𝑎 )
𝑎
=
√2 √5 ax
𝑎
=𝑥√2 √5 =x√2.5 =x=√10𝑥
xyyx 3575 32
 =
√75𝑥2 𝑦3
5√3𝑥𝑦
=
1
5
√75𝑥2 𝑦3
5√3𝑥𝑦
=
1
5
√25𝑥𝑦2 =
1
5
√52 𝑥𝑦2
=
1
5
5𝑦√ 𝑥 =y√ 𝑥
5 233 2
5 nmnm  =
√5𝑚23
𝑛
√𝑚3 𝑛25 =
√(5𝑚215
𝑛)
15
3
√(𝑚3 𝑛2)
15 15
3
=
√(5𝑚215
𝑛)5
√(𝑚3 𝑛2)315 =
√ 55 𝑚10 𝑛515
√𝑚9 𝑛615 =
√5515
𝑚
𝑛
=
√5515
𝑚
√ 𝑛15 =
√5515
𝑚
√ 𝑛15
√𝑛1415
√𝑛1415 =
√55 𝑚𝑛1415
√𝑛𝑛1415 =
√55 𝑚𝑛1415
√ 𝑛1515 =
√55 𝑚𝑛1415
𝑛
=
√3125𝑚𝑛1415
𝑛
4 3226 543
318 zyxzyx  =
√18𝑥3 𝑦46
𝑧5
√3𝑥2 𝑦24
𝑧3
=
√(18𝑥3 𝑦412
𝑧5)
12
6
( √3𝑥2 𝑦212
𝑧3)
12
4
=
√(18𝑥3 𝑦412
𝑧5)2
( √3𝑥2 𝑦212
𝑧3 𝑧)3
=
=
√182 𝑥612
𝑦8 𝑧10
( √33 𝑥612
𝑦6 𝑧9
=
√[(2)(3)(3)]2 𝑥6 𝑦8 𝑧1012
√33 𝑥612
𝑦6 𝑧9
=
√2234 𝑥612
𝑦8 𝑧10
( √33 𝑥612
𝑦6 𝑧9
= √(2)2(3)12
𝑦2 𝑧
= √(4)(3)𝑦212
𝑧 = √12𝑦212
𝑧