Multiplicationofradicals

fab a a bn

IIF and Ta Tb

Simplifiedformofa radical1 Radicand hasnofactorraisedto a powergreater than equaltotheindex

ex I2 Radicanddoesnotcontain a fraction 43 No radicals in thedenominatorofa fraction

ex 2

52

Exz simplify thefollowing

asMaio zerosin In

af i I

Exz simplify 556 I 43 9

a 556 54514 254 4 16F ZEE s a

7 6 36g 49

56 2.2 2.7 237 8 6455654 fi 9 s

lo toob Fy 54.56 121

256 24 12 144

c 6Tso 34 3 9 169

652552 4066 5 Fr3052

d i3 5353,5psFt Fs7 5

e 7 5 7525,52to

7 tl5 35oF127522

Youtryl.ltb fqf6 a2b3

5 1 he356 of Tb b't b356 a bib3a2b

Recall fan aex 3Pa a

Addsubtract radicals

In 3x su n se nn x za

likeradicals havetermswiththesame indexandsaneradicand

a 35 1 7Be 10ThE1srnt7c 153 253 253 Entry f Tutyd ru of 45

B 154 f ife 4 nFy Zafy

s aFy

ft f nastyE seFy

Et 4 358152354521 52652 152 752

b sing 3yF8THfiery 3yFFx 2.3 3 Z

8 n Fk y 3 y n Tn2 1B 3 12

3ayTze2 3 F 3 z

Py Fyry ry

c story l3yEytnyT98y3irEoEiQE.E r

IiE hW

fxyTyJd Add 32ft 58

F EEfzYou try I4F45 sty45955 y255

ll2F y2f

Multiplication property 4 radicalsTaub Va Vb

Ext Multiply the expressiona se tr

3 5 S2 B155121554533oBJ

b very C 7 Fy2n 7

Fy TayN

yruI

yc 3rTf h

tuft y6Th t 3 oilt

t33 fan a

d fftr Ef10 TOTTI 6

14 52Specialcase products

c fattya

Ca b GIb.toa2 ab abtb2a2 zcb b2

Ex Squarethe radial explosion

id 135fdTv tDd 3rd 3rd 19fdt6rd9Ib

i25y sty STE t 225y 10iT

c 2 B 2 CatbCab D beB2

2 2 withradicals

3 4 D a b constant

DivisionofRadicals

t.ae aIaErbFo i x

RationalizeDenominators

a Ef Eff Effi.ir iff.fEfFta2.645.7werationalizebecauseitseasierto dividebyanintegerinthiscase 7

b if Fi Es

t f o

Multiply numerator and denominator

by conjugate ofdenominator

conjugates a b atb because

Cab atb a ababbal b

d ftp.IT.rztoft ff.I y EE 5Ya

ftp.i Fr.KEIFtH YTiIiEI EiiiE 4E

I714441

7F4g

E rs E rs ir

frxt rx

Tx tfs Tx Es coil first5

at b a b d b

Tx Js and Tx Fs are factorsofX 5

In general a b ra of Tat Rb