Question

radical expression.

Answer 1

@DanJS

Answer 2

ok

Answer 3

\[\frac{ 1 }{ 3+\sqrt{5} }\]

Answer 4

so with these problems you said to take the bottom and make a fraction but with opposite signs. Something like that?

Answer 5

yeah, multiply by (3 - root5) / (3 - root5)

Answer 6

So like this:
\[\frac{ 1 }{ 3+\sqrt{5} }*\frac{ 3-\sqrt{15} }{ 3-\sqrt{15} }\]

Answer 7

yeah, cept root 5, not 15's

Answer 8

multiply the bottom together, what you get

Answer 9

woops! didn't mean to write that.

Answer 10

using foil?

Answer 11

\[\frac{ 1 }{ 3+\sqrt{5} }*\frac{ 3-\sqrt{5} }{ 3-\sqrt{5} }\]

yeah the FOIL thing... in general:

(a + b)*(a - b) = a^2 -a*b + a*b - b^2 = a^2 - b^2

Answer 12

\[9-3\sqrt{5}+3\sqrt{5}-\sqrt{5}\sqrt{5}\]

Answer 13

yep

Answer 14

what about the top?? with the 1 and everything.

Answer 15

\[\frac{ 1 }{ 3+\sqrt{5} }*\frac{ 3-\sqrt{5} }{ 3-\sqrt{5} } = \frac{ 3 - \sqrt{5} }{ 9 - 5 }\]

Answer 16

so the bottom ends up to be 4. oh. and the top stays the same. So final answer:
\[\frac{ 3-\sqrt{5} }{ 4 }\]

Answer 17

you can write it like this
\[\frac{ 3 - \sqrt{5} }{ 4} \]or\[\frac{ 3 }{ 4 } - \frac{ 1 }{ 4 }\sqrt{5}\]

Answer 18

Okay! I think my teacher doesn't want them in fractions though so I'll stick to the first one. Thanks! I got to go now but I might be on later tonight. May I just ask one thing....what is in it for you...like is there a benefit for you by helping kids with math? just wondering. Or is it just for the fulfillment of having helped someone?

Answer 19

nothing is in it. I just help out and it helps me remember basic things i might have forgotten. I used to care about the stupid study score, now i just help people who want to learn. and ignore people that just want me to do their homework for them. lol

Answer 20

i will probably go back for a higher degree eventually, i dont want to get bad at the basics

Answer 21

that is super cool of you!