Question

3+sqrt3/3-sqrt3(3+sqrt3/3+sqrt3)
sorry it looks confusing, I'll fix it

Answer 1

\[\frac{ 3+\sqrt{3} }{ 3-\sqrt{3} } (\frac{ 3+\sqrt{3} }{ 3+\sqrt{3} } )\]

Answer 2

pretty sure the next step is 9+6sqrt3+3/9-3 but I don't know how to get that

Answer 3

I think I'm supposed to foil it, but I dunno

Answer 4

(9+3+6sqrt3)/(9-3)

=2 +sqrt3

Answer 5

so you're applying the conjugate...
\[\frac{ (3+\sqrt{3})(3+\sqrt{3)} }{ 9-3 }\]

Answer 6

(a+b)^2 = a2 + b2 +2ab

(a+b)(a-b)= a2 - b2

Answer 7

you are right @koel I'm just having trouble doing the algebra part

Answer 8

3x3 is 9, I get that, but where do the 6 and 3 come from?

Answer 9

(3+sqrt3)^2 = 9 +6 sqrt3 +3

Answer 10

and (3 -sqrt 3)(3+sqrt 3) = 9-3 =6

Answer 11

ok, I kinda see... 3^2 is 9... does the sqrt3^2 = 6?

Answer 12

no sqrt3^2 = 3

Answer 13

ok, where does the 6 come from then?

Answer 14

its the 2ab term because of which 6sqrt3 comes

Answer 15

I'm trying really hard to remember how that equation works. it's been a while. what is it called?

Answer 16

the (a+b)^2...

Answer 17

(a+b)^2 = a^2 + 2ab + b^2

a =3
b=sqrt3

so a^2=9

2ab = 2*3*sqrt3 = 6sqrt3

b^2 = sqrt3^2 =3

Answer 18

i dont think the formula has a name

you can derive it by multiplying

(a+b)(a+b) = a(a+b)+b(a+b)

Answer 19

oh yea! ok, lemme try that