Help pleaseeeeeeeeeeee =*(

- anonymous

Help pleaseeeeeeeeeeee =*(

- katieb

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- anonymous

|dw:1435701198421:dw|

- anonymous

\[\sqrt{\sqrt{\sqrt{3x}}}=\sqrt[6]{3x}\]\]

- anonymous

think that should be a 8 not 6

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## More answers

- anonymous

so you have
\[\sqrt[8]{3x}=\sqrt[4]{2x}\] raise each side to the power of 8

- anonymous

yes

- anonymous

yeah you are right
it should be \(\sqrt[8]{2x}\)
raise each side to the power of 8 to clear the radicals

- anonymous

\[3x=4x^2\] is what you will get
then solve for \(x\)

- anonymous

hey how did u get that....?

- anonymous

raised both sides to the power of 8

- anonymous

wait what? why?

- anonymous

\[\sqrt[8]{3x}^8=3x\]
\[\sqrt[4]{2x}^8=(2x)^2=4x^2\]

- anonymous

why? to get rid of the radicals

- anonymous

but i don't understand why when the base is different numbers

- anonymous

if you want to get rid of the racial on \(\sqrt[8]{3x}\) it should be pretty clear you have to raise it to the power of 8 right?

- anonymous

lol "radical"

- anonymous

no i don't understand that part is that like a rule or something?

- anonymous

when r u allowed to do that? when they're both divisible by the same number?

- anonymous

how else can you do it? you have the eighth root
if you want to get it without the eighth root you have to raise it to the power of 8

- anonymous

what else can you do?

- anonymous

so you just come up with the 8 out of thin air? there isn't a rule or anything?

- anonymous

no , it was the eighth root
if it was the fifteenth root, you would have to do something different

- anonymous

.... omg im so lost and nervous

- anonymous

I'm seriously not understanding that part

- anonymous

how are you going to get the \(3x\) outside of the radical ? you have
\[\sqrt[8]{3x}\]
what can you do to get rid of that radical?

- anonymous

if you square it, you would still have a radical wouldn't you ?

- anonymous

|dw:1435702119282:dw|

- anonymous

actually \(\left(3x\right)^{\frac{1}{8}}\)

- anonymous

okay so how come u get rid of that one but not the right side with the 2x? how come it gets neglected?

- anonymous

oh don't neglect it , it will feel left out
if you raise the left hand side to the power or 8 you have to do the same thing to the right hand side

- anonymous

yes but the right still has a power of 2

- anonymous

\[\sqrt[4]{2x}^8=(2x)^2=4x^2\]

- anonymous

i thought we're trying to eliminate the power

- anonymous

you can't always get what you want
you gotta use what you got

- anonymous

oops
\[3x=4x^2\]

- anonymous

ok... i think i get it.... so what if the right side is not divisible by the number it's divided by on the right side?

- anonymous

on the left side no the rights *

- anonymous

that is an excellent question, best one yet

- anonymous

then i guess you would have to multiply by the least common multiple of the indices

- anonymous

oh ... i'm sorry to be so bothersome but can u please give me n example ? i just really wanna get this question and prepare for future problems like this

- anonymous

so if you had, for example
\[\sqrt[4]{3x}=\sqrt[6]{2x}\] you would have to raise each side to the power of 12 since the least common multiple of 4 and 6 is 12

- anonymous

then both radicals would be gone and you would ge t
\[(3x)^3=(2x)^2\]

- anonymous

ohhhhh hmmmmm

- anonymous

so the objective is to get rid of the fraction power right?

- anonymous

just so happens in this case raising to the power of 8 gets rid of the radical on both sides

- anonymous

yes

- anonymous

ahhhhhhhhhhhhhhhhhhhh i got it!!!!!!! thank you <333333333333333

- anonymous

yw

- anonymous

btw you still have to solve
\[3x=4x^2\]

- anonymous

i got the answer i just needed to know how to do it

- anonymous

one answer is obviously 0 the other you get from solving
\[4x^2-x=0\] etc

- anonymous

oops
\[4x^2-3x=0\]

- anonymous

3/4 = .75

- anonymous

yes

- anonymous

Hey wait one more question.. if the problem was reversed it doesn't matter right? like the 3x was on the right side and the 2x was on the left as long as one of fractions is gone that's the objective no matter the left or right side right?

- anonymous

yeah that has nothing to do with it
of course the answer would be different, but the method would be the same

- anonymous

okay gotcha thank you again <333

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