divide and rationalize 3+sqrt(18)/ 1+sqrt(8)

- anonymous

divide and rationalize 3+sqrt(18)/ 1+sqrt(8)

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- anonymous

hey, how's it going?

- anonymous

hi can you help me?

- anonymous

sure, first do you know how to simplify sqrt(18) and sqrt(8)?

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## More answers

- anonymous

yes i simplified the problem to \[3+3\sqrt{2}/1+2\sqrt{2}\]

- anonymous

good!

- anonymous

when you have a square root in the denominator, to clean it up you have to multiply by something called the conjugate, which basically just means you change the sign of the square root term

- anonymous

i did that too.

- anonymous

so for this case, you would multiply it by (1-2sqrt(2))/(1-2(sqrt(2))

- anonymous

\[1-2\sqrt{2}\] right?

- anonymous

right, so did you multiply the top and bottom by that?

- anonymous

i did but i erased it.

- anonymous

but just foil right? i get the top part but the bottom confuses me.

- anonymous

what confuses you about the bottom part? what did you get for the top?

- anonymous

i got \[3-6\sqrt{2}+6\sqrt{2}-12\] simplified to -9

- anonymous

WHat hold on somyjing looks rwong

- anonymous

thats what i figured i got everything till the foiling part

- anonymous

bob how did you do this

- anonymous

2sqrt(2)*3sqrt(2) is what?

- anonymous

\[6\sqrt{2}\]

- anonymous

well no, that is 12, but you got that part right, your mistake was 3sqrt(2) * 1 i believe

- anonymous

oh your right... i thought i was going to be able to eliminate the roots in the middle...

- anonymous

you want to eliminate the roots on the bottom, that's why are we doing this. you don't have to eliminate the roots on the top.

- anonymous

\[3-6\sqrt{2}+3\sqrt{2}\] -12 right?

- anonymous

looks good for the top

- anonymous

i kept getting 1-8

- anonymous

looks good, so what's your end answer?

- anonymous

hold on i haven't solved it yet, thought you were going to say i was wrong.

- anonymous

where's your confidence? :)

- anonymous

not in my math capabilities thats for sure haha. \[-9-3\sqrt{2}/-7\]

- anonymous

okay so the numbers are right but my text book says all the nubmer are positive.

- anonymous

looks good, don't forget parentheses if you write it like you typed it, and you can multiply by -1/-1 and get rid of all the negatives if you want

- anonymous

parentheses? the ones used to foil? and okay thank you soo much your very helpful.

- anonymous

i was just saying the way you typed your answer, could be -9 - (3sqrt(2)/-7) which is not the same thing

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