Question

Rationalize the denominators.

Answer 1

@phi @mathmale

Answer 2

you need to multiply top and bottom of the fraction by the conjugate of the denominator.

Answer 3

You would get 2⋅3√+5⋅2√3⋅3√−2⋅2√=6√+2

Answer 4

@dako87

Answer 5

\[3\sqrt{3}+2\sqrt{2}\]

Answer 6

the conjugate has same terms but different sign
the product will be rational

Answer 7

Sorry read this wrong, rationalizing the denominators would get you this answer 3(3√)−2(√2) @dako87

Answer 8

(3√ 3+ 2√2 )( 3√3 - 2√2)
= 27 + 6√6 - 6√6 - 8)

can you continue?

note that the 2 middle terms cancel out

Answer 9

you lost me at conjugate lol

Answer 10

the 2 middle terms equal zero so you are left with

27 - 8

Answer 11

you get the conjugate by changing the sign in the middle thats all

eg
conjugate of 3 - √2 is 3 + √2

Answer 12

and when you multiply these you lose the square root terms and are left with a rational number

Answer 13

heres a simple one
(1 + √2)(1 - √2) = 1*1 + 1*√2 - 1*√2 - 2) = 1 - 2 = -1

Answer 14

follow?

Answer 15

yes so far so good

Answer 16

so back to the problem the denominator = 27 - 8 = 19

so now you neeed to multiply the numerator by 3√3 + 2√2

Answer 17

ok thank you i think i can handle it from here

Answer 18

ok