Squares Squareroots Factorization Scert[1]

8/16/2019 Squares Squareroots Factorization Scert[1]

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à í Z g §M - d J ©A m{U d J ©‘ yi ( Squares and Square-roots)

à mË¶ { j H$

- 1 g o‘ r ~ mO yMooM m¡ag V wH$S>oK o. V o‘ m§S>y>Z EH$ ^ ard Mm¡ag ~ Z d . Mma >V wH$S>oK oD $Z O moS>b o V a A g mMm¡ag ~ Z V mo. 4 h mH$moU Ë¶ mg §» ¶ oMmd J ©A mh o? J wU mH$mamV A m{U

2 d J © é n mV {b h r . 4 = 2 x 2 = 2

- h mH$moU Ë¶ mg §» ¶ oMmd J ©A mh o? J wU mH$mamÀ¶ mA m{U d J m©À¶ mé n mV

{b h r.

- h mH$moU Ë¶ mg §» ¶ oMmd J ©A mh o? J wU mH$mamÀ¶ mA m{U d J m© À¶ mé n mV

{b h r.

- qMMmoHo‘ m§S>y>Z / M m¡H$Q>rÀ¶ md h rV Mm¡ag a§J d yZ 3 x 3 Mm Mm¡ag ~ Z d . EHyU H${H$V r

qMM moHo d mn ab oqH$d m{H$V r Mm¡ag a§J d b o? h mV rZ Mm d J ©A mh o.

- d arb à ‘ mU o7 Mm d J ©e moY .- 16 qMMmoHo‘ m§S>y>Z / Mm¡H$Q>rÀ¶ md h rV 16 Mm¡ag a§J d yZ Mm¡ag ~ Z d d d J © g §» ¶ m {b h r.

- Mm¡H$Q>rÀ¶ mH$mJ Xmd a H$moU Ë¶ mh r EH$md J © g §» ¶ oMm Mm¡ag a§J d yZ XmI d .

- 36 Mm¡ag V wH$S>o‘ m§S>y>Z EH$ Mm¡ag V ¶ ma H$a. Ë¶ mMr ~ mO y{H$V r A mb rµ?

- H$°b ³ ¶ wb oQ>a d mn ê $Z 36 Mo‘ yi A d ¶ d n mS>y>Z d J ©‘ yi H$mT>y>Z XmI d .

( {e j H$m§À¶ mg §X^ m© g mR>r H¥V r - ‘ wb m§Z m n {h ë ¶ m H$mh r ‘ yi g §» ¶ m ‘ mh rV A g ë ¶ m n m{h O oV .

n {h b r ‘ yi g §» ¶ m2. H$°b ³ ¶ wb oQ>ad a n wT>rb à ‘ mU oH$am -

36 / 2 = 18 18 / 2 = 9

A mV m9 b m2 Z o^ mJ O mV Z mh r åhU yZ A mV m3 Z o^ mJ m¶ Mo.

9 / 3 = 3 3 / 3 = 1

å h UyZ 36 Mo‘ yi A d ¶ d 2 x 2 x 3 x 3 . ¶ mV r b g §» ¶ m§À¶ mO moS>ç mH$ê $Z 36 M o d J © ‘ yi 6)

- H$°b ³ ¶ wb oQ>a d mn ê $Z 196 Mo‘ yi A d ¶ d n mS>y>Z d J ©‘ yi H$mT>y>Z XmI d .Copyleft - NLF-MSCERT Squares-Sq-roots-factorization- page 1


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V mo|S>r

- d rg n ¶ © ªVÀ¶ m‘ yi g §» ¶ måhU yZ XmI d .

- EH$ V od rg g §» ¶ m§Mod J ©åh U yZ XmI d .

b oI r

1) [aH$må¶ mO mJ r ¶ mo½¶ g §» ¶ m { b h r .

2) EH$mM g §» ¶ oÀ¶ mJ wU mH$mamÀ¶ mé n mV {b h ÿZ d J ©ê $n mV A m{U d J ©‘ yi é n mV {b h r.

3) ‘ yi A d ¶ d n mS>y>Z d J ©‘ yi {b h r. ( ‘ yi A d ¶ d m§Mr C Xmh aU on wT>o{Xb ob r A mh oV )

=x=2

3 3 3 9

=x=2

2

=x=2

10

=x=2

20

9 = 3= x =2

33 39

= x =16

= x =25

= x =64

25 =

16 =

36 =

49 =

Copyleft - NLF-MSCERT Squares-Sq-roots-factorization- page 2


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4) 1 V o10 Mon mT>o¶ mMm¡H$Q>rV

{b h r.

Ë¶ mV rb g d ©d J ©g §» ¶ m

a§J d .

5) J wU mH$mamMr Mm¡H$Q> n Õ V d mn ê $Z 12 Mmd J ©H$mT>y>Z XmI d b mA mh o. Ë¶ mn Õ V rZ o11 V o

20 g §» ¶ m§Mmd J ©H$mT>.

6) n wT>rb n ¡H$s H$moU V r g §» ¶ m6 À¶ md J ©‘ yi mÀ¶ mO d i A mho? H$°$b ³ ¶ wb oQ>a dmnê$Z R>ad.

7) n wT>rb n ¡H$s H$moU V r g §» ¶ m6 À¶ md J ©‘ yi mÀ¶ mO d i A mho? H$°$b ³ ¶ wb oQ>a dmnê$Z R>ad.

(a) 1.5 (b) 2 (c) 2.5 (d) 3

(a) 2.5 (b) 2.4

1

2

3

4

5

6

7

8

9

10 2 0

3

4

6

8

1 0

1 2

1 4

1 6

1 8

2 4 5 6 7 8 9

100

1 0

6

8

1 0 1 2 1 4 1 6 1 8 2 0

10 x 10 = 100

10 x 2 = 20

2x10=20

2x2=4

210

10

2

X

100 20

20 4

100 20 20 4144

+



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8) EH$ ~ mO y1 g o‘ r A m{U Xþg ar ~ mO y2 g o‘ r A g b ob mEH$ H$mQ>H$moZ {Ì H$moU A mb oI

H$mJ Xmd a H$mT>. Ë¶ mÀ¶ mH$U m©Mr A §XmO ob m§~ r ‘ moO . ( Ë¶ mg mR>r X þ‘ S>b oë ¶ mA mb oI

H$mJ XmMr ~ Z d b ob r ‘ moO n Å>r d mn aV m¶ oB©b .) h r g §» ¶ mH$moU Ë¶ mg §» ¶ oÀ¶ md J ©‘ yi mÀ¶ m

O d i A mh o? A §XmO H$a A mU {U H$°b ³ ¶ wb oQ>aZ oV n mg yZ n h m.

9) EH$ ~ mO y3 g o‘ r A m{U Xþg ar ~ mO y4 g o‘ r A g b ob mH$mQ>H$moZ {Ì H$moU H$mT>y>Z d arb

Ë¶ mg mR>r H¥V r H$a.

10) 30 Mod J ©‘ yi H$moU Ë¶ mXmoZ g §» ¶ m§À¶ m ‘ Ü¶ oA mh o?

(a) 2 d 3 (b) 3 d 4 (c) 4 d 5 (d) 5 d 6 (e) 6 d 7.



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‘ yi A d ¶ d (Prime Factors)

n yd ©V ¶ mar

- a§J d b ob oMm¡H$m¡Z d Ë¶ m§MoJ Q> n mh ÿZ J wU mH$ma {b h r. C Xm.

à . 1 3 x 2

à . 2 3 x 2 x 2

à . 3

3 x 2 x 2 x 2

à . 4

à . 5

à . 6



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à . 7

à . 8

à . 9

à . 10

à 11

à . 12



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à . 13 ‘ yi g §» ¶ m§À ¶ m J wU mH$ma ê $n mV {b h r.

6 = 3 x 2

à . 14 ‘ yi g §» ¶ m§À ¶ m J wU mH$ma ê $n mV {b h r.

à . 15 ‘ yi g §» ¶ m§À¶ mJ wU mH$ma é n mV {b {h Ê¶ mg mR>r A md í ¶ H$ V oWoA m¶ V mMog ‘ mZ

^ mJ H$a. d Ë¶ mZ §V a J wU mH$ma é n mV {b h r.3 x 2 x 2

à . 16 ‘ yi g §» ¶ m§À¶ mJ wU mH$ma é n mV {b {h Ê¶ mg mR>r A md í ¶ H$ V oWoA m¶ V mMog ‘ mZ^ mJ H$a. d Ë¶ mZ §V a J wU mH$ma é n mV {b h r.





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à . 19 2 Z o^ mJ O mV moH$m, 3 Z o^ mJ O mV moH$m, 5 Z o^ mJ O mV moH$m¶ mà ‘ mU o

V n mg V n wT>rb g §» ¶ m‘ yi A d ¶ d m§À¶ mJ wU mH$mamÀ¶ mé n mV {b h r.

1) 15 = 3 x 5

2) 20 = 2 x 10

= 2 x 2 x 5

3) 25 =

4) 50 =

5) 12 =

6) 16 =

7) 24 =

8) 30 =

9) 45 =

10) 60 =



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à . ‘ yi A d ¶ d n mS>A m{U A d ¶ d m§À¶ mO moS>ç mH$ê $Z d J ©‘ yi e moY .

1) 144 = 2 x 72 = 2 x 2 x 36

= 2 x 2 x 2 x 18 = 2 x 2 x 2 x 2 x 9 = 2 x 2 x 2 x 2 x 3 x 3 = (2 x 2 x 3) x ( 2 x 2 x 3) = 12 x 12

2) 576 =

3) 3025 =

4) 9801 =

5) 10404 =

20

144 = 12


Squares Squareroots Factorization Scert[1]

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