Name
Date
Class
Reteach
LESSON
11-8 Multiplying and Dividing Radical Expressions
Use the Product and Quotient Properties to multiply and divide radical expressions.
Product Property of Square Roots
Quotient Property of Square Roots
b
Multiply 6 10 .
Product Property of Square
Roots
60
Simplify
Multiply the factors in the
radicand.
4 15
4 15
3
10
3
3
3 30
____
9
Simplify.
Quotient Property
10 ___
3
____
Product Property of Square
Roots
2 15
___3 .
10 ____
10
___
Factor 60 using a perfect
square factor.
b
A quotient with a square root in the
denominator is not simplified. Rationalize
the denominator by multiplying by a form of
1 to get a perfect square.
6 10
6 10
a ___
a
__
; where a 0 and b 0
a b ; where a 0 and b 0
ab Multiply by form of 1.
Product Property
30
____
3
Simplify.
Multiply. Then simplify.
1. 3 12
2. 5 10
3. 8 11
5 2
6
2 22
Rationalize the denominator of each quotient. Then simplify.
7
4. ___
2
2
8
5. ___
3
2
3
12
6. ____
5
3
5
5
14
____
2 6
____
2 15
_____
2
3
5
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c11-8_rt.indd 62
62
Holt Algebra 1
12/26/05 8:26:56 AM
Process Black
Name
Date
Class
Reteach
LESSON
11-8 Multiplying and Dividing Radical Expressions (continued)
Terms can be multiplied and divided if they are both under the radicals OR if they are both
outside the radicals.
Multiply 5 4.
5
2 43 206
Multiply 2 3 .
Multiply 3 6 8 . Write the product
in simplest form.
Use FOIL to multiply binomials with square
roots.
Multiply 3 2 4 2 .
3 (6 8 )
3 (6) 3 8
63 24
FOIL.
Multiply.
12 3 2 42 2
Simplify.
14 7 2
Product Property of
Square Roots
63 26
12 3 2 42 4
Factor 24 using a
perfect square factor.
6 3 4 6
3 4 32 42 2 2
Multiply the factors in
the radicand.
6 3 4 6
3 2 4 2 Distribute.
Add.
Simplify.
Multiply. Write each product in simplest form.
7. 5 4 8 5
4
8. 2 2 14 5 8
4 5 210
2 2 7
9. 6 3 5 3 6 5
6 3 3 5
3 3 27 3
10. 5 10 8 10 50 1310
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c11-8_rt.indd 63
63
Holt Algebra 1
12/26/05 8:26:57 AM
Process Black
*À>V̈ViÊ
--"
££‡n -ULTIPLYINGAND$IVIDING2ADICAL%XPRESSIONS
*À>V̈ViÊ
--"
££‡n -ULTIPLYINGAND$IVIDING2ADICAL%XPRESSIONS
-ULTIPLY7RITEEACHPRODUCTINSIMPLESTFORM
^
^
^
^
^
qq ^
Ó Ó qq
^
{ q ^
{ q q
q
q ™ ^
^
^
ÎÊr xÊÊ
^
^
^
^
qSqD
^
^
^
^
qSqDq SD
qSqDq SqTD
^
^
qq ^
^
qqT
^
^
^
^
^
^
^
^
^
q
?????
^
q B
^
^
q q q ^
^
^
q ????
^
q
q ???
^
q ^
^
È
^
Êr xÊÊ
£ÇÊÊÊr ÎÊÊ
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
œÌʏ}iLÀ>Ê£
*À>V̈ViÊ
--"
££‡n -ULTIPLYINGAND$IVIDING2ADICAL%XPRESSIONS
^
^
^
^
^
^
^
ÈÊÊÈÊÊr ÎÊÊ
^
^
^
ÇÊÊr ÓÊÊÊÓÊÊr ÇÊÊ
^
^
^
^
q
^
q
^
^
^
^
^
r
q
^
S D
q q q
^
Ê £xÊ
ÊÊÊ
ÚÚÚÚ
Ê Ê
Êr
x
^
ÊÊ
Ê Ê Ê
Î
£
Ê
Ê
£ÓX
q ?????
^
qX
^
Ê
ÎX
M
???????
q
^
q M
^
^
^
q q
È
^
q q
^
xÊr ÓÊÊ
S D
^
S D
^
ÊÚÚÚÚ
ÊxÊrÎÊÈÊÊÊÊÊ
ÓÊr ÓÓÊÊ
^
4HEAREAOFARECTANGLEISqY D&INDTHEWIDTHIFTHE
^
LENGTHISqYD
^
^
q Êr ÎÊÊ
???
^ ^ Êr ÎÊÊ
q
ÊÊÊ
ÚÚÚÚ
ÊÊr £{Ê
Ê Ê
Ó
^
q Êr xÊÊ
????
^ Êr^
q
xÊÊ
^
^
£ÓÊrÎÊÊʓÊÓÊ
S D
^
^
q Êr ÓÊÊ
???
^ ^ Êr ÓÊÊ
q
^
3IMPLIFY
2ATIONALIZETHEDENOMINATOROFEACHQUOTIENT4HENSIMPLIFY
^
&INDTHEAREAOFATRIANGLEWHOSEBASEISGIVENBYTHEEXPRESSION
^
^
qMANDWHOSEHEIGHTISGIVENBYTHEEXPRESSIONq M
^
^
^
ÓÊrÎX
ÚÚÚÚÚ
Ê
^
q q
ÊÊ
Êr ÈÊX
ÚÚÚÚ
Ó
^
^
ÊrÓÓX
ÚÚÚÚÚ
^
qX
???????
^ q ^
^
Ê ÓÊ
ÚÚÚ
Ê ÊÊÊ
Êr
Ó
^
Î
0RODUCT0ROPERTY
-ULTIPLY4HENSIMPLIFY
q ????
^
q
q
????
^
q ^
ÓÊr ÈÊÊ
ÚÚÚÚ
q ????
^
q
q ?????
^
X
q
^
q ???
^
q ^
-ULTIPLYBYFORMOF
^
q
????
^
^
q
????
^ 3IMPLIFYEACHQUOTIENT
q ???
^
q 1UOTIENT0ROPERTY
^
q
????
???
q
^ ^
3IMPLIFY
q ^
^
q
????
???
^ q
0RODUCT0ROPERTYOF3QUARE
2OOTS
^
n{ÊÊ£nÊÊr ÎÊÊ
^
qq
Sq D ^
3IMPLIFY ???
&
ACTORUSINGAPERFECT
SQUAREFACTOR
ΙÊÊ£ÎÊÊr ÎÊÊ
^
!QUOTIENTWITHASQUAREROOTINTHE
DENOMINATORISNOTSIMPLIFIED2ATIONALIZE
THEDENOMINATORBYMULTIPLYINGBYAFORMOF
TOGETAPERFECTSQUARE
-ULTIPLYTHEFACTORSINTHE
RADICAND
q
^
^
0
RODUCT0ROPERTYOF3QUARE
2OOTS
q
^
Sq DSqD
£ÎÊÊÎÊÊr £xÊÊ
1UOTIENT0ROPERTYOF3QUARE2OOTS
^
^
^
^
£ÊÊÎÊÊr xÊÊ
^
ÎxÊÊÈÊÊr xÊÊ
^
^
^
œÌʏ}iLÀ>Ê£
^ ^
A
WHEREAANDB
??
A ???
q^
B
qB
qq
^
Sq
qDSq q D
Sq DSqD
^
ÊÚÚÚ
ÊÊr{ÈÊÊ ÊÊÊ
^
^
^
ÎÊÊÎÊÊr ÓÊÊ
^
x
-ULTIPLYr r SqDSq D
^
^
^
Ó{Xr ÓÊÊ
^
qSq qD
^
ÎZ
K
??????
q^
q K
ÚÚÚÚÚÚ
ÊÓÊr £ä
Ê
Ê ÝÊ
ÊÊ
A qBWHEREAANDB
ABq^
q
^
ÓÊÊr £xCÊÊ{ÊÊr ÎÊÊ
^
qSqD
^
Ê ÈZ
Ê
ÚÚÚÚ
Êr
^
q X
????
^
q
^
^
^
^
^
qSqCqD
^
^
£Ç
qXqX
ÈXr
£xÊÊ
^
qSqD
^
q ?????
^
q Z
Ê Î{Ê
ÊÊÊ
ÚÚÚÚ
Ê Ê
Êr
0RODUCT0ROPERTYOF3QUARE2OOTS
{ä
^
£Óx
£äT
^
q
????
^
q
^
>
^
ÚÚÚÚÚ
Ê
ÊÊrÓÈT
qXqX
^
^
^
Sq
D Ê Ê
ÊÊ
££
,iÌi>V…
--"
££‡n -ULTIPLYINGAND$IVIDING2ADICAL%XPRESSIONS
Sq
D ÈÊr£{ÊÊ
Ê
5SETHE0RODUCTAND1UOTIENT0ROPERTIESTOMULTIPLYANDDIVIDERADICALEXPRESSIONS
^
qq
xÊrÎÊÊ
^
q ?????
^
q T
^
Ê ££äÊ
Ê
r
ÚÚÚÚÚ
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
-ULTIPLY7RITEEACHPRODUCTINSIMPLESTFORM
qq
{È
^
Ê >Ê
ÚÚÚ
Êr
Ê ÊÊÊ
^
^
q ????
^
q
^
^
ÊÊÊ
ÚÚÚÚ
Ê Ê
ÊÊr ÎäÊ
£x
q ????
^
q A
^
Sq DSqD
^
^
Ê £äxÊ
ÊÊÊ
ÚÚÚÚÚ
Ê Êr
Ê
^
Sq DSq D
^
nB
^
ÓnÊÊÊr ÓÊÊ
^
£ÎÊÊÓÊÊr ÓÊÊ
^
ÚÚÚÚÚÚ
ÊÊr £äB
Ê
Î
Î
q ????
^
q ^
ÊÊÊ
ÚÚÚÚ
Ê Ê
ÊÊr ÎÎÊ
x
^
^
Sq DSqD
^
Ê ÎÊ
ÚÚÚ
Ê ÊÊÊ
Êr
q
^
q ÓB
{ qB
^
^
ÊÊÊ
ÚÚÚÚ
Ê Ê
ÊÊr £xÊ
^
^
q
q Î ^
Sq DSqD
^
ÓB
q
????????
?????
Î
q ????
????
^ ^
^
q q
???
???
^ ^
^
xÊÊÓÊÊr ÎÊÊ
ÎÊÊr£äÊÊ
3IMPLIFYEACHQUOTIENT
^
q ???
^
q ^
^
q ????
^
q ^
^
^
^
Êr £äÊÊÊÊr ÎäÊÊ
^
^
Sq DSqD
qSq qD
^
Êr ÓÊÊÊ£ä
^
^
^
^
Êr £äXÊ
ÊÓX
xÊÊr ÓMÊÊÓÊÊr £äÊÊ
^
ÓÊÊr ÈÊÊÊÈÊÊr ÎÊÊ
3IMPLIFYEACHQUOTIENT
q ???
^
q
^
qSq qD
^
ÇÊÊÊr ÎxÊÊ
^
^
^
^
^
{ÊÊr ÈÊÊÊ{
^
^
qXSq qXD
^
^
^
qSqMqD
^
Sq DSq D
^
^
xÊÊnÊÊr xÊÊ
^
qSq qD
^
^
Êr £{ÊÊÊxÊr ÓÊÊ
^
£äBr
ÓÊÊ
^
^
qSqqD
^
qSq D
™ÊÊxÊr xÊÊ
^
Ón
^
qSq D
^
ÓÊr ÎÊÊÊÎÊrÓT
^
^
qBqB
^
ÈYr £xÊÊ
^
nXr
ÎxÊÊ
Sq
D ^ ^
qYq
Y
^
^
q SXDSXD
x{
^
^
q ÇÊr xÊÊ x
^
^
ÓÊr£xÊÊ
^
^
qSq D
ÎÊr£äÊÊ
^
Sq DSq D
^
ÎÊr ÓÊÊÊÓÊr ÎÊÊ
£ÓXr
£{ÊÊ
^
qXqX
qq
^
^
qq
^
™ä
^
^
^
^
qXqX
^
^
qSqqTD
^
^
^
^
Sq
D q
ÎäTr
ÓÊÊ
^
^
^
^
^
q £ää TÊ Ê
^
^
^
Sq
D ^
xÊrÓÊÊ
^
qSTDSTD
^
qT
^
Ó
Ón
qq
^
qq
qTqT
^
-ULTIPLY7RITEEACHPRODUCTINSIMPLESTFORM
^
^
Sq
D q q
ÊÊÊ
ÚÚÚÚ
ÊÓÊrÊÈÊÊ
Î
^
ÊÊÊ
ÚÚÚÚÚ
ÊÓÊr £xÊ
Ê Ê
x
^
r
Ê £äÊÊÞ`
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
AK4up.indd 89
œÌʏ}iLÀ>Ê£
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
89
œÌʏ}iLÀ>Ê£
Holt Algebra 1
12/26/05 8:02:35 AM
,iÌi>V…
--"
££‡n -ULTIPLYINGAND$IVIDING2ADICAL%XPRESSIONSCONTINUED
…>i˜}i
--"
££‡n )RRATIONAL2OOTSOF1UADRATIC%QUATIONS
4HESOLUTIONSOFAQUADRATICEQUATIONARESOMETIMESCALLEDROOTSBUTTHAT
HASNOTHINGTODOWITHWHETHERORNOTTHESOLUTIONCONTAINSASQUAREROOT
)FASOLUTIONDOESCONTAINASQUAREROOTITISCALLEDANIRRATIONALROOT
4ERMSCANBEMULTIPLIEDANDDIVIDEDIFTHEYAREBOTHUNDERTHERADICALS/2IFTHEYAREBOTH
OUTSIDETHERADICALS
^
)SXq ANIRRATIONALROOTOFXX
3UBSTITUTEANDSIMPLIFYTOFINDOUT
-ULTIPLY
^
^
^
^
Sq DSq
Dq ^
^
Ó
9iÃÆÊÊÊTxÊÊÊr ÎÊÊEÊ ÊÊ£äÊÊTxÊÊÊr ÎÊÊEÊÊÓÓÊÊÊ
^
^
ÊTÓnÊÊ£äÊr ÎÊÊEÊÊÊTxäÊÊ£äÊr ÎÊÊEÊÊÓÓÊÊä
5SETHE1UADRATIC&ORMULATOFINDALLROOTSOFXX
$OESTHISSUPPORTYOURANSWERTOQUESTION
^
-ULTIPLYq q ^
^
^
-ULTIPLYr Tr E7RITETHEPRODUCT
INSIMPLESTFORM
^
5SE&/),TOMULTIPLYBINOMIALSWITHSQUARE
ROOTS
^
^
-ULTIPLYTrETrE
^
q q
^
^
^
q q
q
^
^
^
^
q q ^
^
^
SDq qq q ^
^
^
^
^
^
^
^
q q q q q ^
q 0RODUCT0ROPERTYOF
3QUARE2OOTS
q q q
^
&/),
-ULTIPLY
3IMPLIFY
!DD
^
^
^
^
^
ÊÊÊÊÊÚÚ
£ÊÊÎÊ
ÚÚÚÚÚÚÚÚ
Êr ÓÊÊ
Ê£Ê ÊÊÚÚ
ÊÎÊr ÓÊÊÆÊÞiÃ]ÊXÊÊ£ÊÊÎÊr ÓÊÊʈÃÊNOTʜ˜iʜvÊ̅iÊÌܜÊÀœœÌð
Ó
Ó Ó
XÊÊÊÊ
,OOKATTHEROOTSTHATYOUFOUNDINQUESTIONSAND"ASEDONTHESE
FEWEXAMPLESCOMPLETETHESECONJECTURESABOUTTHEIRRATIONALROOTS
OFQUADRATICEQUATIONSTHATHAVERATIONALCOEFFICIENTS
^
^
^
qSq qD
B )FONEROOTISMNÊq^
PTHENTHEOTHERROOTIS
q { q Êr^
nÊÊ
^
^
{Êr xÊÊÓÊr £äÊÊ
^
%XPLAINHOWTHE1UADRATIC&ORMULAGUARANTEESTHATYOURCONJECTURESIN
QUESTIONWILLHOLDTRUEANYTIMEAQUADRATICEQUATIONHASIRRATIONALROOTS
^
ÓÊÊÓÊr ÇÊÊ
^
SqDSq D
SDS
^
^
^
^
x DSDS Êr ÎÊÊDqS x Dq S Êr ÎÊÊD
^
^
SqDSq D
^
xäÊ£ÎÊr £äÊÊ
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
/…iʵÕ>`À>̈VÊvœÀ“Տ>ʈ˜VÕ`iÃÊÊõÕ>ÀiÊÀœœÌÆʈÀÀ>̈œ˜>ÊÀœœÌÃÊ܈Ê>Ü>ÞÃÊ
LiÊVœ˜Õ}>Ìið
2ECALLTHATWHENTHEDISCRIMINANTSBACDISGREATERTHANZEROTHERE
ARETWOREALSOLUTIONS7HATMUSTBETRUEABOUTTHEDISCRIMINANTFOR
THERETOBETWOIRRATIONALSOLUTIONS
^
ÓÇÊr ÎÊÊ
Vœ˜Õ}>ÌiÃ
OFEACHOTHER
MÊÊNr^
PÊ
A )NGENERALTHEIRRATIONALROOTSARE
^
^
-ULTIPLY7RITEEACHPRODUCTINSIMPLESTFORM
q
SqD
^
Ó
œÆÊ{ÊÊT£ÊÊÎÊrÓÊÊEÊ ÊÊ{ÊÊT£ÊÊÎÊr ÓÊÊEÊÊ£ÇÊÊÊ
^
^
^
ÊTÇÈÊÊÓ{Êr ÓÊÊEÊÊÊÊT{ÊÊ£ÓÊr ÓÊÊEÊ£ÇÊÊxxÊÊ£ÓÊr ÓÊÊÊqÊä
5SETHE1UADRATIC&ORMULATOFINDALLROOTSOFX X
$OESTHISSUPPORTYOURANSWERTOQUESTION
3IMPLIFY
q q
^
)SXqANIRRATIONALROOTOFXX
3UBSTITUTEANDSIMPLIFYTOFINDOUT
^
Sq DSqD
^
^
XÊÊxÊÊÊrÎÊÊÆÊÞiÃ]ÊXÊÊxÊÊÊrÎÊÊʈÃʜ˜iʜvÊ̅iÊÌܜÊÀœœÌð
^
$ISTRIBUTE
-ULTIPLYTHEFACTORSIN
THERADICAND
&ACTORUSINGA
PERFECTSQUAREFACTOR
q q ^
^
œÌʏ}iLÀ>Ê£
ÊBÊÓÊÊ{ACÊܜՏ`ʅ>ÛiÊ̜ÊLiÊ}Ài>ÌiÀÊ̅>˜ÊâiÀœÊ>˜`ÊNOTÊ>Ê«iÀviVÌÊõÕ>Ài°
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
œÌʏ}iLÀ>Ê£
*ÀœLi“Ê-œÛˆ˜}
--"
££‡n -ULTIPLYINGAND$IVIDING2ADICAL%XPRESSIONS
,i>`ˆ˜}Ê-ÌÀ>Ìi}ˆiÃ
--"
££‡n 5SE-ODELS
7RITEEACHCORRECTANSWERASARADICALEXPRESSIONINSIMPLESTFORM
5SETHEFOURMODELSBELOWASAGUIDETOMULTIPLYINGANDDIVIDINGRADICAL
EXPRESSIONS
^
7MODELSTHE
4HEEXPRESSION ??
2
ELECTRICALCURRENTINAMPERESWHERE7
ISPOWERINWATTSAND2ISRESISTANCE
INOHMS(OWMUCHELECTRICALCURRENT
ISRUNNINGTHROUGHANAPPLIANCEWITH
WATTSOFPOWERANDOHMSOF
RESISTANCE
q
4HEDIAGRAMSHOWSTHEDIMENSIONSOF
ADININGTABLE7ITHALEAFINPLACETHE
TABLEEXPANDSTOSEATEIGHTPEOPLE
'- &%^c#
ÚÚÚÚ
ÊÊ>“«Ã
ÊxÊrÊxÊÊÊ
Ó
&INDTHEAREAOFTHETABLE
Ê«iÀˆ“iÌiÀ\ÊnÊr ÎÊʓ
^
$ISTRIBUTIVE
0ROPERTY
^
^
^
^
^
^
^
^
^
^
^
^
q q q ^
^ ^
q q q
qq
^
q q
q {{nÊr£xÊÊÊ{ÎÓÊr ÓÊÊˆÊ˜Ê Ê
^
4HEVOLUMEOFWATERINALAKEINGALLONS
^
CANBEREPRESENTEDBYXq (EAVY
RAINSAREFORECAST4HEVOLUMEOFWATER
^
ISEXPECTEDTOINCREASEq TIMES(OW
MANYGALLONSOFWATERAREEXPECTEDIN
THELAKEAFTERTHERAIN
& ??
X GALLONS
' XGALLONS
^
( Xq GALLONS
* XGALLONS
! FT
" FT ^
# q FT
$ q FT 4HEAREAOFARECTANGULARWINDOWIS
^
SQUAREFEET4HELENGTHISqFEET
7HATISTHEWIDTHOFTHEWINDOW
4HEHEIGHTOFATRIANGLECANBEFOUND
USINGH???
!WHERE!ISTHEAREAAND
B
BISTHEBASEOFTHETRIANGLE7HICH
SHOWSTHEHEIGHTOFATRIANGLEWITHAN
^
^
AREAOFqCMANDABASEOFq CM
WRITTENINSIMPLESTFORM
^
^
& qCM
( qCM
^
! q
FEET
# qFEET
" FEET
$ qFEET
^
^
' qCM
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
AK4up.indd 90
^
^
???
^ q ^
q
???
^ ???
^
q q
^
????
q
^
q
^
q
???
#OMPLETETHEFOLLOWING
2*LIVESINASTUDIOAPARTMENT4HE
APARTMENTISRECTANGULARWITHAWIDTH
^
OFq FEETANDALENGTHOF
^
q FEET7HATISTHEAREAOF
2*SAPARTMENT
^
^
qq q Ó
3ELECTTHEBESTANSWER
^
^
SqDSqD
^
q q q
^ ^
q
X qq
^
Xq
^
Xq
2ATIONALIZINGTHE
$ENOMINATOR
&/),
SqD
q
^
&INDTHEAREAOFTHETABLEWITHTHE
^
ADDITIONOFALEAFTHATMEASURESq ^
INCHESBYq INCHES
^
^
^
^
qX
{{nÊr £xÊʈʘÊÓÊ
>Ài>\Ê£ÓÊʓÊÓÊ
^
q Xq X
^
2ILEYSNEWBEDROOMISAPERFECTSQUARE
^
%ACHSIDEMEASURESq METERS
&INDTHEAREAANDPERIMETEROF2ILEYS
BEDROOM
4WO3QUARE
2OOTS
- +^c#
^
-ULTIPLYINGAND$IVIDING2ADICAL%XPRESSIONS
^
* q CM
œÌʏ}iLÀ>Ê£
7HICHMETHODWOULDBEUSEDTOMULTIPLYSqD "
7HATDOESITMEANTOhRATIONALIZETHEDENOMINATORv
,iÜÀˆÌiÊ̅iÊiÝ«ÀiÃȜ˜ÊÜÊ̅iÀiʈÃʘœÊõÕ>ÀiÊÀœœÌʈ˜Ê̅iÊ`i˜œ“ˆ˜>̜À°
-ULTIPLY7RITEEACHPRODUCTINSIMPLESTFORM
^
^
^
^
^
^
qSqD
qq £nÊrÓÊÊ
^
^
xÊr ÎÊÊÊÓÊr ÈÊÊ
^
^
xÊrÓÊÊ
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
90
{
xnÊÊÓÊr xÊÊ
3IMPLIFYEACHQUOTIENTBYRATIONALIZINGTHEDENOMINATOR
^
q
???
?????
^
^ q q
^
Sq DSq D
^
X
????
q
^
q ^
ÚÚÚ
ÊÊr X
Ê Ê
Ó
œÌʏ}iLÀ>Ê£
Holt Algebra 1
12/26/05 8:03:10 AM