<PRE><B>Question 140776</B>
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(3)/(sqrt(6) - 2)}}} * {{{(sqrt(6) + 2)/(sqrt(6) + 2)}}} = {{{(2sqrt(18) + 4sqrt(3))/(6 - 4)}}} = {{{(2sqrt(18) + 4sqrt(3))/2}}}
:
2 will cancel into 2 and 4 giving us:
{{{sqrt(18) + 2sqrt(3)}}}
:
Factor 18 to reveal a perfect square, extract 3:
{{{sqrt(9*2) + 2sqrt(3)}}} = {{{3sqrt(2) + 2sqrt(3)}}}
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