SOLUTION: Hi could someone please help me, I have an Expression that needs rationalizing by taking the conjugate: 3√10/6-8√3 it says the answer is -3√10-4√30/26 B

Algebra ->  Square-cubic-other-roots -> SOLUTION: Hi could someone please help me, I have an Expression that needs rationalizing by taking the conjugate: 3√10/6-8√3 it says the answer is -3√10-4√30/26 B      Log On


   



Question 558608: Hi could someone please help me, I have an Expression that needs rationalizing by taking the conjugate:
3√10/6-8√3
it says the answer is -3√10-4√30/26 But I got nothing like this, here is what I tried:
I multiplied the top and bottom by the conjugate of the denominator 6-8√3, which I thought was 6+8√3.
So I did this:
3√10/ *6+8√3 = 18√10+8√3*3√10/
6-8√3 *6+8√3 36-64*3
Obviously this is not even close to the correct answer, could someone please explain to me all the steps I need to do and where I am going wrong.
Many Thanks Jim.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3√10/6-8√3
it says the answer is -3√10-4√30/26 But I got nothing like this, here is what I tried:
I multiplied the top and bottom by the conjugate of the denominator 6-8√3, which I thought was 6+8√3.
So I did this:
3√10/ *6+8√3 = 18√10+8√3*3√10/6 = (18sqrt(10) + 24sqrt(30))/6
= (3sqrt(10)+4sqrt(30)
--------------
6-8√3 *6+8√3 = 36-64*3 = 36 - 192 = -156
-----------------------------
Your symbols cause too much confusion.
3sqrt%2810%29%2F%286-8sqrt%283%29%29
= 3sqrt%2810%29%2A%286%2B8sqrt%283%29%29%2F%28-156%29
= %2818sqrt%2810%29+%2B+24sqrt%2830%29%29%2F%28-156%29
= -%283sqrt%2810%29+%2B+4sqrt%2830%29%29%2F26