Question 936095
{{{(3+sqrt(24))/(6*sqrt(8))}}}



{{{(3+sqrt(4*6))/(6*sqrt(4*2))}}}



{{{(3+sqrt(4)*sqrt(6))/(6*sqrt(4)*sqrt(2))}}}



{{{(3+2*sqrt(6))/(6*2*sqrt(2))}}}



{{{(3+2*sqrt(6))/(12*sqrt(2))}}}



{{{((3+2*sqrt(6))*red(sqrt(2)))/(12*sqrt(2)*red(sqrt(2)))}}} Multiply top and bottom by {{{sqrt(2)}}} to rationalize the denominator.



{{{(3*sqrt(2)+2*sqrt(6)*sqrt(2))/(12*sqrt(2)*sqrt(2))}}} Distribute



{{{(3*sqrt(2)+2*sqrt(6*2))/(12*sqrt(2*2))}}}



{{{(3*sqrt(2)+2*sqrt(12))/(12*sqrt(4))}}}



{{{(3*sqrt(2)+2*sqrt(4*3))/(12*sqrt(4))}}}



{{{(3*sqrt(2)+2*sqrt(4)*sqrt(3))/(12*sqrt(4))}}}



{{{(3*sqrt(2)+2*2*sqrt(3))/(12*2)}}}



{{{(3*sqrt(2)+4*sqrt(3))/(24)}}}



So, {{{(3+sqrt(24))/(6*sqrt(8))=(3*sqrt(2)+4*sqrt(3))/(24)}}}



Which means the answer is <font color="red">Choice A</font>

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