Post on 07-Apr-2022
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