rationalize the denominator?

Question

rationalize the denominator.

1) 18√24 / -3√8

2) -24√45 / 72√20

Answer 1

1. 18sqrt24 = 18*2sqrt6 = 36sqrt6
-3sqrt8 = -3*2sqrt2 = -6sqrt2

Divide and get -6*sqrt3

2. -24*sqrt45 = -24*3sqrt5 = -72sqrt5

72*sqrt20 = 72*2sqrt5 = 144sqrt5

Dividing, the square root 5 cancels, leaving you with -72/144 =
-1/2

Answer 2

=18√24 / -3√8
= 18√4*6 / -3√4*2
= 18√4√6 / -3√4√2
= cancel the two √4 and 18 divide by -3 becomes -6
then -6√6 / √2
simplify √6 in this way
= -6√3*2 / √2
= -6√3√2 / √2
now cancel the √2's u will get
-6√3


now question 2

= -24√45 / 72√20
= divide -24 / 72 u will get -1/3 and simplify the two √45 and √20
= -24√9*5 / 72√4*5
= simplify √9 and √4 and 24/72 u will get
= -3√5 / 3√5√4
cancel the two 3's and √5 and find √4 which is ofcourse 2

u will be left with

-1/2 i.e -negative half

hope that helps
bye
Deepak

Answer 3

1) 18√24 / -3√8=-6√3



2) -24√45 / 72√20=-(1/3)√(9/4)=-(1/3)(3/2)=-1/2

Answer 4

1) 18*sqrt(24) / (-3*sqrt(8)) * sqrt(8)/sqrt(8) =
18*sqrt(192) / -24

2) -24*sqrt(45) / 72*sqrt(20) * sqrt(20)/sqrt(20) =
-24*sqrt(900) / 1440

Answer 5

1) Multiply the top and bottom by radical 8, then simplify.
2) Multiply the top and bottom by radical 20, then simplify.