Question

cubed root 5/3x

Answer 1

Need clarification! Do you want the cube root of [5/(3x)]? This can certainly be done, but note that neither 5 nor (3x) is a perfect cube.

Answer 2

hey mathmale :)

\(\huge\color{ blue }{\huge {\bbox[5pt, cyan ,border:2px solid black ]{ a^{B/C}~=~\sqrt[C]{a^B} }}}\)

Answer 3

making it a perfect cube. this is in the subject of radicals

Answer 4

Oops blurted out, sorry it was irrelevant I am blind

Answer 5

LOL thats okay Solomon!

Answer 6

multiply

Answer 7

yes, times cube root of 5². top and bottom

Answer 8

Yes. Multiply by what?

Answer 9

5?

Answer 10

so multiply by 5^2?

Answer 11

You have (3x) in the your denominator. What would you have to do to this (3x) to transform it into a perfect cube?

You can answer this yourself. If you multiply your denominator, (3x), by 5, do you obtain a perfect cube?

Answer 12

You should be focusing on the denominator, not on the numerator.

Answer 13

oh :( thank you mathmale

Answer 14

You have (3x) in the your denominator. What would you have to do to this (3x) to transform it into a perfect cube?

Answer 15

i think you said to do 3 times 5

Answer 16

Ask yourself: "What does 'perfect cube' actually mean?

What are some examples of perfect cubes?

Answer 17

uhm i guess a 3?

Answer 18

But TFL, 3 is not a perfect cube, is it?

Is 7 a perfect cube? 8? 9? 28?

Answer 19

3^2*x^2

Answer 20

9 is

Answer 21

Now you're on the right track. If you multiply (3x) by 3^2*x^2, you DO get a perfect cube. Congrats.

Answer 22

Now, begin with the whole fraction 5/(2x). Multiply both numerator and denom. by your 3^2*x^2. What do you get?

Answer 23

my teacher just told me :( but thanks A LOT to mathmale and SolomonZelman!

Answer 24

thank MM

Answer 25

9 mathmale?

Answer 26

do you mind if I call you that ?

Answer 27

MM

Answer 28

or Mister Math male → MMM ?

Answer 29

Glad to be of help. @solomzonzelman: Hello! You can call me anything you want that has a decent sound to it. Omit the mister and concentrate on the mm. :)

Answer 30

so is it 9?

Answer 31

okay, then. m&m :P

Answer 32

!tealfitlove:\

Here's what I was suggesting:
\[\frac{ 5 }{ 3x }\frac{ (3x)^2 }{ (3x)^2 }\] Please simplify the math here.

Answer 33

not sure

Answer 34

x is not part of the denominator in the original question, is it ?

Answer 35

Keep in mind: You are trying to make the given denominator, (3x) into a perfect cube.

Answer 36

:(

Answer 37

Actually, @tealfitlove wants to find the cube root of 5/(3x). so, yes, x is part of the deonom.

Answer 38

well right now the question has been narrowed down to 3^2*x^2

Answer 39

Multiply this out: (3x)(3^2*x^2_.

Answer 40

324?

Answer 41

\[\frac{ 5 }{ 3x }\frac{ (3x)^2 }{ (3x)^2 }=\frac{ 5(9x^2) }{ (3x)^3 }\]

Answer 42

Remember, you have an 'x' in the denom. and MUST deal with it.

Is the denom. now a perfect cube? Yes or no. Why?

Answer 43

i have no idea.

Answer 44

3^3 is a perfect cube; 2^3 is also; (38y^7)^3 is also. So, try again. is (3x)^3 a perfect cube?

Answer 45

yes

Answer 46

Right. It is.

Answer 47

so the answer is (3x)^3?

Answer 48

What is the cube ROOT of\[\frac{ 5 }{ 3x }\frac{ (3x)^2 }{ (3x)^2 }=\frac{ 5(9x^2) }{ (3x)^3 }?\]

Answer 49

now we have cubedrooty^3=y

Answer 50

Up to now, all our work focused on transforming 5/(3x) into a fraction with a perfect cube denominator (not numerator). Only now are we going to try to find the cube root of that transformed expression.

Answer 51

We are to find\[\sqrt[3]\frac{ 5(9x^2) }{ (3x)^3 }\]

Answer 52

and that can be simplified as\[\sqrt[3]\frac{ 45x^2 }{ (3x)^3 }\]

Answer 53

It is very important that you recognize that \[\sqrt[3]{27}=\sqrt[3]{3^3}=3\]

Answer 54

Please simplify:\[\sqrt[3]\frac{ 45x^2 }{ (3x)^3 }\]

Answer 55

yes

Answer 56

Please do it. Find / write the cube root of the numerator.
Then find the cube root of the denominator.

Answer 57

Note how the denominator of \[\sqrt[3]\frac{ 45x^2 }{ (3x)^3 }\]

Answer 58

looks very much like\[\sqrt[3]{3^3}\]

Answer 59

which you presumably now know how to evaluate / reduce / simplify.