SOLUTION: Rationalize the denominator. (3√10)/(2+√10) I so far got... (3√10)/(2+√10) * (2-√10)/(2-√10) [(3√10)(2+√10)]/(2)^2+(√10)^2

Algebra ->  Radicals -> SOLUTION: Rationalize the denominator. (3√10)/(2+√10) I so far got... (3√10)/(2+√10) * (2-√10)/(2-√10) [(3√10)(2+√10)]/(2)^2+(√10)^2      Log On


   

Question 1058504: Rationalize the denominator.
(3√10)/(2+√10)
I so far got...
(3√10)/(2+√10) * (2-√10)/(2-√10)
[(3√10)(2+√10)]/(2)^2+(√10)^2
[(6√10)-(3√100)]/4-10
Then I get stuck.
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
3sqrt%2810%29%2F%282%2Bsqrt%2810%29%29

The conjugate of the DENOMINATOR is 2-sqrt%2810%29. Multiply the rational expression (the ENTIRE fraction) by 1.


Simplify that.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Rationalize the denominator.
(3√10)/(2+√10) 

I so far got...

(3√10)/(2+√10) * (2-√10)/(2-√10)     - Correct

[(3√10)(2+√10)]/(2)^2+(√10)^2        - Wrong //  Must be %28%283%2Asqrt%2810%29%29%2A%282-sqrt%2810%29%29%29%2F%282%5E2+-+%28sqrt%2810%29%29%5E2%29

[(6√10)-(3√100)]/4-10                - Correct.

Now replace sqrt%28100%29 by 10 and replace (4-10) by (-6).


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalize the denominator.
(3√10)/(2+√10)
I so far got...
(3√10)/(2+√10) * (2-√10)/(2-√10)
[(3√10)(2+√10)]/(2)^2+(√10)^2
[(6√10)-(3√100)]/4-10
Then I get stuck. 
%286sqrt%2810%29+-+3sqrt%28100%29%29%2F%284+-+10%29 <======= You're up to here

%286sqrt%2810%29+-+3%2810%29%29%2F%28-+6%29%29 -------- Simplifying matrix%281%2C3%2C+sqrt%28100%29%2C+and%2C+4+-+10%29

%286sqrt%2810%29+-+30%29%2F%28-+6%29

%28-+6%28-+sqrt%2810%29+%2B+5%29%29%2F%28-+6%29 ------- Factoring NUMERATOR

%28cross%28-+6%29%28-+sqrt%2810%29+%2B+5%29%29%2Fcross%28%28-+6%29%29 ------ Canceling - 6 in NUMERATOR and DENOMINATOR

highlight_green%28matrix%281%2C3%2C+-+sqrt%2810%29+%2B+5%2C+or%2C+5+-+sqrt%2810%29%29%29