SOLUTION: Hi, Well I've run into a problem that I can't really do. The question is to rationalise 1/(cube root 2 - 1). The answer is cube root 2 + cube root 4 + 1. I know how to ration

Algebra.Com
Question 973570: Hi,
Well I've run into a problem that I can't really do.
The question is to rationalise 1/(cube root 2 - 1). The answer is cube root 2 + cube root 4 + 1. I know how to rationalise 1/cube root 2 but I'm not sure how to do this one. What I got is:
1/cube root 2-1=1/cube root 2-1 * (cube root 2^2 + 1)/(cube root 2^2 + 1)
And I've so on and so forth, but I didn't get the right answer. I got cube root 4 + 1.
Thanks
Found 2 solutions by MathTherapy, greenestamps:
Answer by MathTherapy(10801)   (Show Source): You can put this solution on YOUR website!
Hi,

Well I've run into a problem that I can't really do.

The question is to rationalise 1/(cube root 2 - 1). The answer is cube root 2 + cube root 4 + 1. I know
how to rationalise 1/cube root 2 but I'm not sure how to do this one. What I got is:

1/cube root 2-1=1/cube root 2-1 * (cube root 2^2 + 1)/(cube root 2^2 + 1)

And I've so on and so forth, but I didn't get the right answer. I got cube root 4 + 1.

Thanks
*************************************************
If this is , then your 1st answer, "cube root 2 + cube root 4 + 1," is WRONG, but the 2nd, "cube
root 4 + 1," is CORRECT!! See BELOW!!

 =  
 *  ---- Rationalizing denominator by MULTIPLYING numerator and denominator by  =  
 =  =  =  =  =  =

Answer by greenestamps(13325)   (Show Source): You can put this solution on YOUR website!


Use this factoring pattern:



With and , this becomes



Your expression is



To rationalize the denominator, you need to multiply numerator and denominator by



Then



... which is the answer you say you are supposed to get
RELATED QUESTIONS

IN response to the answer give for Question 201790 This problem is actually cube root (answered by jim_thompson5910)
how to solve= 1/cube root 4+ cube root 2 +1 i know the ans is cube root 2 -1 but i... (answered by Alan3354,jsmallt9)
Dear Sir/Madam, I am confronted with the following problem: "T varies directly as... (answered by longjonsilver)
My question is: what is the cube root of x -5=3 From what I understand cube root is the (answered by tutor_paul)
Hi, I've been out of school for 2 years and I cannot remember how to do the cube root of (answered by Edwin McCravy)
Hi. How do I prove that this is an identity?? I really don't get how this works...... (answered by AnlytcPhil)
I'm using a book called No-Nonsense Algebra by Richard Fisher. I've run into a problem... (answered by MathLover1,math_helper)
Hi, I've tried solving this equation in multiple ways but can't seem to crack it. The... (answered by MathLover1,josgarithmetic,greenestamps)
Good afternoon guys. Here is my question: Simplify: _____... (answered by Alan3354)