SOLUTION: What is the solution to two square root of three over square root of six minus two?

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Question 140776: What is the solution to two square root of three over square root of six minus two?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
What is the solution to two square root of three over square root of six minus two?
:
Multiply expression by the conjugate of the denominator
FOIL,the middle terms cancel in the denominator, so you eliminate the radical
2sqrt%283%29%2F%28sqrt%286%29+-+2%29 * %28sqrt%286%29+%2B+2%29%2F%28sqrt%286%29+%2B+2%29 = %282sqrt%2818%29+%2B+4sqrt%283%29%29%2F%286+-+4%29 = %282sqrt%2818%29+%2B+4sqrt%283%29%29%2F2
:
2 will cancel into 2 and 4 giving us:
sqrt%2818%29+%2B+2sqrt%283%29
:
Factor 18 to reveal a perfect square, extract 3:
sqrt%289%2A2%29+%2B+2sqrt%283%29 = 3sqrt%282%29+%2B+2sqrt%283%29