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 ->  Square-cubic-other-roots -> 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      Log On


   

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(10858) About Me  (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 1%2F%28root+%283%2C+2%29+-+1%29, then your 1st answer, "cube root 2 + cube root 4 + 1," is WRONG, but the 2nd, "cube
root 4 + 1," is CORRECT!! See BELOW!!

1%2F%28root+%283%2C+2%29+-+1%29 = 1%2F%28-+1+%2B+root+%283%2C+2%29%29 
1%2F%28-+1+%2B+root+%283%2C+2%29%29 * %28-+1+-+root+%283%2C+4%29%29%2F%28-+1+-+root+%283%2C+4%29%29 ---- Rationalizing denominator by MULTIPLYING numerator and denominator by -+1+-+root+%283%2C+2%5E2%29 = -+1+-+root+%283%2C+4%29 
 =  = %28-+1+-+root+%283%2C+4%29%29%2F%28%28-+1%29%5E2+-+root+%283%2C+2%2A4%29%29 = %28-+1+-+root+%283%2C+4%29%29%2F%28%28-+1%29%5E2+-+root+%283%2C+8%29%29 = %28-+1+-+root+%283%2C+4%29%29%2F%281+-+2%29 = %28-+1+-+root+%283%2C+4%29%29%2F%28-+1%29 = highlight%281+%2B+root+%283%2C+4%29%29%29

Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


Use this factoring pattern:

a%5E3-b%5E3=%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29

With a=root%283%2C2%29 and b=1, this becomes

2-1=%28root%283%2C2%29-1%29%28root%283%2C4%29%2Broot%283%2C2%29%2B1%29

Your expression is

1%2Froot%283%2C2%29

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

%28root%283%2C4%29%2Broot%283%2C2%29%2B1%29

Then



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