2.18 fP PgtU(Algebraic Surds):

 

UU CzsAi 1.7 g PgtU v CU AS gSAi ï UgwĪz Pwzê. E dUtvP AAz PgtU U PAiİzê.

 

F CzsAiz GAiVĪ ZgPgUz (x, a, b, n.) EUɯ sP ASU.

Pgt: Ezg m - PgtP(order) n PgtAi(radicand)

 

S: PgtUĒ CU Įsgƥz MAz P v PgtAiU Azg, CU gƥ PgtU(Like surds).

Įsgƥz PgtAi PU Cx PgtAiU g g DVzg. CU C gƥ PgtUɣߪgĒ(unlike surds).

 

Gz: PɼV PgtU UĤ:

1.

2.

 

ð PgtU ĮsgƥP vgzg, CU Cgƥ PgtUɣߨQv. KPAzg CU PgtP MAz DVzg, PgtAiU g g (48, 12). DzjAz PgtU VPjĪ z CU CvAv Įs gƥP vgP. DzjAz ð Jgq PgtU gƥPgtU CU Pgt P 2, PgtAi 3.

 

3.-- PgtP = 3, PgtAi=2

4. -- PgtP = 4, PgtAi =5

F Jgq PgtU PgtP/PgtAiU g gAiiV. DzjAz EU CgƥPgtU.

PɼV QAiU UĤ:-

1. 5a+3a =(5+3)a =8a

2. 7a-2a =(7-2)a= 5a

PgtU AP v P UAi iqvê.

 

1. įs gƥzgĪ gƥ PgtU AS UtPU AP Cx P ir, PgtU v Cx v qAivê.

 

2.18 ĸ1: ĮsgƥP v:

 

jg:

 

2.18 ĸ 2. ĮsgƥP v:

 

jg:

=== 2x (1+1/2)

= 2x3/2

 

2.18 ĸ 3. Aiģ Az Pɬj.

 

jg:

() ()

=

=

 

UĤ:-

 

2. (ab) n= an *bn AiĪzAvAi, AiĪĪ Cĸjzê.

 

2.18 ĸ 4. jAz Ut¹.

 

jg:

=51/2= 52/4= (52)1/4= (25)1/4

=(25)1/4* 31/4= 751/4=

K irzê?

PgtU Ut¸ĪU CĸjĪ AvU:-

Av1 : PgtAiģ WvA gƥz gɬj.

Av 2 : PgtPU ..C PAqĻrj.

Av 3 : PgtU MAz PgtP(Av 2 gAv) gĪAv jw

Av 4 : AiĪĪߣĸj, PgtAiU Ut¹.

 

2.18 ĸ 5. jAz Ut¹.

 

jg:

 

A.

Av

gu

1

= 31/3, =21/4

PgtAiģ WvA gƥz gɬj.

 

2

PgtU PgtPU 3 v 4. EU ..C = 12

PgtPU ..C PAqĻrj.

3

= 31/3= 34/12 = (34)1/12 = (81)1/12

PgtU WvA (1/12) zĹ

4

=21/4 = 23/12 =23/12 = (23)1/12 = (8)1/12

PgtU WvA (1/12)zĹ

5

() *( ) =

 

 

 

Ez MAz CsU AS. F sU ASAiģV iqĪz U?

jAz Ut¸Ī.

* = = 5. 5 MAz sU AS.

S:

MAz PgtAiģ vAz Pgt¬Az Ut¹, sU ASAiģ qAiĪ QAiU PgtUCPgtPgt(Rationalisation) JAz ɸg.

DU D PgtAi PngĪ PgtU CPgtPgP(rationalizing factor )(RF) DVgvz.

ð GzguAiİ JAz g CPgtPgP.

 

2.18 ĸ 6: Ezg CPgtPgP Aiiz?

 

jg:

zv ĸAiİ iv CsU sU. 6 JAz sU AS.DzjAz VU PVgĪz Ai CPgtPgP

Ai CPgtPgP: KPAzg,

(1/3+2/3 = 3/3)

* = = (a-b)

FU, Aiģ Az Ut¹.

svA:- 6(a-b)1/3*((a-b)2)1/3

= 6(a-b)1/3*(a-b)2/3

= 6(a-b)(1+2)/3 = 6(a-b) sU AS.

 

S: Jgq PgtU Cx MAz sU AS, vAz Pgt EU v (Cx v) z Pgt(binomial surd) Jߪg.

Gz: , ,

MAz z PgtAiģ vAz z Pgt¬Az Ut¹zU, sU AS Azg. MAz vAzg AAiV(CPgtPgP)(Conjugate) Jvê.

 

z Pgt*AAiV=sU AS.

 

2.18 ĸ 7 : Ai AAiVAiģ PAqĻr.

 

jg:

= 2()

FU, (a+b) (a-b) = a2-b2 v U Uwz.

DzjAz Ai zv PgtAi AAiVAiiV vgvz.

*

= 2()*()

= 2{()2-()2}

= 2{22*()2-()2`}

= 2(4x-y) =8x-2y - Ez sU AS.

 

PgtAi ggƥzzU, bz CPgtPgtUƽ PɼV AvU Cĸjvê:

 

1) bzz CPgtPgP PAqĻrAiĨP.

2) bzz CPgtPgP zv PgtAi CA v bzUgqP Ut¸P.

 

2.18 ĸ 8: bz CPgtPj ĮsgƥP v: 2/()

 

jg:

()*() =(x-y) ( (a-b)(a+b) = a2-b2 v a = b =)

Ez bzz CPgtPgP(AAiV).EzjAz CA v bzUgqP Ut¸Ī.

2/()

={2/()}*{()/()}

=2 ()/(x-y)

 

2.18 ĸ 9: bz CPgtPj ĮsgƥP v: ()/()

 

jg:

ð GzguAiAvAi g CPgtPgP

()/()

= {()/()}*{()/()}

= ()*()/(9*2-5) (()2=9*2 and ()2=5)

= ()/13

=()/13

= ()/13

 

2.18 ĸ 10 : bz CPgtPj Įs gƥP v: 7/ () - / ()

 

jg:

EgĪ Jgq zU vPV CPgtPjĪ.

1. z zz CA v bz g AAiVAiiz jAz Ut¹:

()*() = 10-3 =7

7/ () = 7*()/(()*())

= 7()/7 (* = 3)

= 3+

 

2. FU Jgq z CPgtPjĪ. CA v bzUgq g AAiVAiiz jAz Ut¹

/ ()

=*()/(6-2)

=/4

= /2

 

7/ () - / ()

= (3+) - /2

= (6+ 2 -+)/2

= (6++)/2

 

 

2.18 Pv SAU

 

 

 

AS

ɣqPz CAU

1

2

MAz PgtAiģ vAz Pgt¬Az Ut¹ sU ASAiģ qAiĪ QAiU PgtU CPgtPgt Jߪg.