Question

rationalize the denominator, then simplify:
8/ 3sqaure root of 2

Answer 1

is this \[\frac{8}{\sqrt[3]{2}}\]?

Answer 2

yess

Answer 3

if so, you may want to say "cube root of 2" to make it clearer.

Answer 4

ohh okay, sorry i forgot that

Answer 5

No that can't be right. I think it's square root. Not cubic root.

Answer 6

Oh okay. I guess it is.

Answer 7

idk?

Answer 8

ok then you want the denominator to be a perfect cube, so multiply by
\[\frac{\sqrt[3]{4}}{\sqrt[3]{4}}\] because then you will get the cube root of 8 in the denominator, and that is 2

Answer 9

Is it \[3 * \sqrt{2}\]
or is it \[\sqrt[3]{2}\]

The first means "3 times the number which, when multiplied by itself, gives 2"
The second means "the number that, when cubed, gives 2."

Answer 10

so your answer is
\[\frac{8}{\sqrt[3]{2}}\times \frac{\sqrt[3]{4}}{\sqrt[3]{4}}\]
\[=\frac{8\sqrt[3]{4}}{\sqrt[3]{8}}\]
\[=\frac{8\sqrt[3]{4}}{2}=4\sqrt[3]{4}\]

Answer 11

Ah okay. Well then multiply by sqrt(2) / sqrt(2)

Answer 12

okay thank you two so much. (:

Answer 13

That gives you
(8*sqrt(2)) / (3 * sqrt(2)^2) =
(8sqrt(2)) / (3*2) =
(8sqrt2) / 6

Answer 14

My pleasure =)

Answer 15

@smoothmath why could it not be
\[\sqrt[3]{2}\]?

Answer 16

Um... because I asked her and she said that it's not?

Answer 17

i am not saying it is or isn't i am just asking how you know

Answer 18

i certainly don't know, it could be either.

Answer 19

Meg did you delete your reply? I could have sworn she replied clarifying that is was 3*sqrt(2)

Answer 20

no it actually was \[\sqrt[3]{2}\]

Answer 21

@meg it is one of the two answers above. depends on the question really

Answer 22

oh ok. then it is
\[4\sqrt[3]{4}\]

Answer 23

Haha oh okay. Yes. What satellite did. Not me.

Answer 24

i accidently said the other one. but i appreciate both of you helping. (:
@satellite thanks yours was the answer. an @smooth thank you anyways. lol.

Answer 25

i have a ton of these problems for homework. but i dont understand the m too well.. @SmoothMath & @satellite73

Answer 26

post and you will get answers for sure
please though remember that
\[\sqrt[4]{x}\] is the "fourth root" of x, not 4square root x

Answer 27

alright thank you ! (:

Answer 28

Meg, basically the idea is to first "rationalize" the denominator.
That's just fancy talk for "get rid of the radical on the bottom."

Answer 29

Now we know we can multiply the fraction by 1 and not change it's value, so we multiply by some fraction with the same thing on top and bottom.