Question

@satellite73

Answer 1

To write it in the simplest radical form, we would first multiply the top and bottom by sqrt(2)
and we would get:
3sqrt(2)
-------
sqrt(16)
(sqrt(16) can be simplified) Which is also equal to:
3sqrt(2)
------- <---- Answer
4
Why I multiplied it by sqrt(2), was to have a perfect square which is 16 and can be simplified to 4.



A little question for you:

Why is 3sqrt(2) / 4 more exact than 3 / sqrt(8) ?




ESSAY FEEDBACK

good start here but you don't have the square root of 16 you have square root of 64 and that equals 8. Then on the top you also need to multiply by square root of 8. The rule is you can not ever have a fraction with a square root denominator or zero or negative.

Answer 2

essay feedback is full of crap

Answer 3

The rule is you can not ever have a fraction with a square root denominator

ok fine, that it to put something is "simplest radical form" not to make it more "exact"

Answer 4

Well, I'll text my teacher and see what she says.

Answer 5

if i recall correctly, the original question was
\[\frac{3}{\sqrt{8}}\] right?

Answer 6

Yes

Answer 7

@satellite73 lolz! full of crap..

Answer 8

ok lets make sure we understand this, even if your teacher does not

Answer 9

your goal is to get rid of the radical in the denominator, and at the moment you have \(\sqrt8\) down there

Answer 10

you could certainly multiply top and bottom by \(\sqrt{8}\) if you like
you would get
\[\frac{3\sqrt{8}}{8}\] but that is not in simplest radical form either because \(\sqrt{8}=\sqrt{2^3}\) and \(3>2\) i.e. the power inside the radical is greater than the index of the radical (which is 2 for square root)

Answer 11

in order to put this in simplest radical form, you would have to then write
\[\frac{3\sqrt{8}}{8}=\frac{3\times 2\sqrt2}{8}\] then cancelling the 2 top and bottom gives
\[\frac{3\sqrt{2}}{4}\]

Answer 12

but the only reason we had to take that stupid step is because you misguided teacher is a slave to a wrong procedure
the way you clear a radical is not to multiply by whatever you see in the radicand, it is to make the radicand a perfect square

Answer 13

if i see
\[\sqrt{8}\] i can easily make it in to \(\sqrt{16}=4\) by multipying by
\(\sqrt{2}\)
no need to multiply by \(\sqrt{8}\) to get \(\sqrt{64}\) as 16 is just as good of a perfect square as 64 is
better in fact, because now i don't have to reduce

Answer 14

Do you mind if I showed this to my teacher?

Answer 15

ask your teacher why he or she things you need to multiply by \(\sqrt{8}\) when \(\sqrt{2}\) will do
i would love to know the response
maybe ask why \(\sqrt{8}\) instead of \(\sqrt{512}\) because if you do that, you would bet
\[\sqrt{4096}=64

Answer 16

well i am ranting, because slaves to method is the very worst in math education, showing not only limited knowledge, but an attitude towards math that i find anathema, not to mention destructive to students

but you don't need to rant
you can edit if you like, and simply explain that the best procedure is to multiply by the smallest number that will produce a perfect square inside the radical, not just some number, or the number that you see there

Answer 17

I know this is your opinion, but it does explain it all.

Answer 18

i, however, will copy and paste your teachers response in to my new folder of really bad math questions (and answers)

Answer 19

yeah well edit out the "stupid math teacher" part
you need a good grade, i do not

Answer 20

Alrighty, thank you again!

Answer 21

you might gently ask what exactly "simplest radical form" means and i would love to know the response if any
and also ask if "simplest radical form" is a synonym for "exact" (it isn't)

Answer 22

Well I asked her two questions, I will see what she says then ask her those two.

Answer 23

Probably won't get a reply til tomorrow.

Answer 24

let me know
maybe you will get a nice reply saying "oh yes, i see you are quite right"
somehow i doubt it

Answer 25

Haha, I would be very fluttered in laughter if she replied like that.