February 7, 2018

Multiplying radical expressions

consider:

= 3.4=12

if6

= VT = 12

÷-

. 131-27 = -2 .

3=-6it# = PIIE = - 6

February 7, 2018

Rule for multiplying radical expressions

IF =-2 IF

If Kaand IT arere@n#sthenVF . Vfb = Has

February 7, 2018

Simplify the following:

: 1/-6.8 = 1/4-8 = 11-16-3

not real = VI. By = 403

= iyz . 58 = if = 4i

= ¥25 = Pts = - 5

February 7, 2018

Simplifying radicals

Examples

xff.tl#xOI=V3FoFxe=5x2yzT=

2×62=13/-8.9×3

= YET

=2xy3F =Xy3TsI

February 7, 2018

Simplifying products of radical expressionsb d

=

13/54=5×2×3%4- #×3

= $-270 ×5y>

×2

= *ftp.qq#==3xyyitFxI1 3xy2 Ptoxy( y2) 3

February 7, 2018

Simplifying products of radical expressions

=

6111K¥= 6ftp.3xyi- -

=

6.7×1/113=421×3141115

February 7, 2018

Dividing radical expressions

Consider

and

So...

VF = # =3

I I €⇐5T=§

February 7, 2018

Rule for dividing radical expressions

If Fa and AT are

real numbers and b¥0

then Fa#=iFb

9

February 7, 2018

Simplify the following: ×x÷= X5 '2=×3

→

. .=lF¥xfiEI←= PIFII

OH,F÷⇒÷3I←r

→ Rationalizing the

7Denomina=To rationalize the denominator

means rewrite the expressionSo that there are no

radicals in the denominatorand no denominators in

any radical .

Notational :¥23 or ifs

Rationalize the

denominator'

÷¥it÷*±BE ±Te=±Ex4

- Ptzx Plax1¥= KEY .mx#nz*E*= 3k¥

February 7, 2018

February 7, 2018

February 7, 2018

February 7, 2018

sixty-

V5FxTy"

YEEE'

*¥x23

February 7, 2018

Rationalize the denominator