Rationalize the denominators.

Question

dako87 · Answer

attachment

dako87 · Answer

@phi  @mathmale

welshfella · Answer

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

onyxxelite · Answer

You would get 2⋅3√+5⋅2√3⋅3√−2⋅2√=6√+2

onyxxelite · Answer

@dako87

welshfella · Answer

$$3\sqrt{3}+2\sqrt{2}$$

welshfella · Answer

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

onyxxelite · Answer

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

welshfella · Answer

(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

dako87 · Answer

you lost me at conjugate lol

welshfella · Answer

the 2 middle terms equal zero so you are left with

27 - 8

welshfella · Answer

you get the conjugate by changing the sign in the middle thats all 

eg 
 conjugate of 3 - √2   is 3 + √2

welshfella · Answer

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

welshfella · Answer

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

welshfella · Answer

follow?

dako87 · Answer

yes so far so good

welshfella · Answer

so back to the problem  the denominator = 27 - 8 = 19 

so now you neeed to multiply the numerator by 3√3 + 2√2

dako87 · Answer

ok thank you i think i can handle it from here

welshfella · Answer

ok