SOLUTION: Rationalize the denominator. Let cr = cube root. 5/(cr(2)) Let me see. 5/(cr(2)) • (cr(2))/(cr(2)) 5(cr(2))/(2) The book's answer is different.

Algebra ->  Square-cubic-other-roots -> SOLUTION: Rationalize the denominator. Let cr = cube root. 5/(cr(2)) Let me see. 5/(cr(2)) • (cr(2))/(cr(2)) 5(cr(2))/(2) The book's answer is different.       Log On


   

Question 1207360: Rationalize the denominator.

Let cr = cube root.

5/(cr(2))

Let me see.

5/(cr(2)) • (cr(2))/(cr(2))

5(cr(2))/(2)
The book's answer is different.

P. S. How do I upload math photos (geometric figures, graphs of functions, etc) on this site?

Found 5 solutions by mananth, math_tutor2020, Edwin McCravy, greenestamps, MathTherapy:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
5/(cr(2)


5*cr(4)/2
OR
5*cr(2^2))/2

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

5%2F%28root%283%2C2%29%29

=

=

= %285%2Aroot%283%2C2%2A2%29%29%2F%28%28root%283%2C2%29%29%5E3%29

= %285%2Aroot%283%2C4%29%29%2F%282%29

Therefore,
5%2F%28root%283%2C2%29%29=%285%2Aroot%283%2C4%29%29%2F%282%29

In the second step we multiply top and bottom by two copies (not one copy) of root%283%2C2%29. This is so the denominator will end up with 3 copies of root%283%2C2%29 to lead to %28root%283%2C2%29%29%5E3+=+2

As far as I'm aware, students aren't allowed to directly upload photos to the algebra.com website.
You can instead upload the photo to some photosharing website and then post the link.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalize the denominator.
Let cr = cube root.
5/(cr(2))
5%5E%22%22%2Froot%283%2C2%29%22%22=%22%22%22%22=%22%225root%283%2C4%29%2Froot%283%2C2%5E3%29%22%22=%22%225root%283%2C4%29%2F2%5E%22%22

Let's use "cr" instead of the standard root%283%2C%22%22%29

5%5E%22%22%2Fcr%282%5E%22%22%29%22%22=%22%22%22%22=%22%225%2Acr%282%5E2%29%2Fcr%282%5E3%29%22%22=%22%225%2Acr%284%5E%22%22%29%2F2%5E%22%22

Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I'll go ahead and use your notation of cr(2) to represent the cube root of 2.

The given expression has cr(2) in the denominator. In the work you show, you multiplied numerator and denominator by cr(2). But cr(2) times cr(2) does not rationalize the denominator. You need to multiply numerator and denominator by cr(2) twice to make the denominator rational.

(5/cr(2)*(cr(2)/cr(2))*(cr(2)/cr(2)) = (5*cr(2)*cr(2))/2 = 5cr(4)/2

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalize the denominator. 

Let cr = cube root.

5/(cr(2))

Let me see.

5/(cr(2)) • (cr(2))/(cr(2))

5(cr(2))/(2)

The book's answer is different.

P. S. How do I upload math photos (geometric figures, graphs of functions, etc) on this site? 


When root%28n%2CR%29 is rationalized, it becomes: root%28n%2C+R%29 * root%28n%2CR%5E%28n+-+1%29%29.
matrix%281%2C1%2C+5%2F%28root%283%2C2%29%29%29
 ----- Rationalizing denominator by multiplying numerator & denominator by root%283%2C2%5E%283+-+1%29%29


** Note that: Denominator