Question 163465
{{{(2sqrt(6))/(sqrt(72)/4)}}}
Start multiplying numerator and denominator by 4:
{{{((2sqrt(6))/(sqrt(72)/4)) * (4/4)}}}
{{{ (8sqrt(6))/(sqrt(72))}}}
Now, factor the stuff under the radical:
{{{ (8sqrt(2*3))/(sqrt(2*2*2*3*3))}}}
Pull out "pairs" from underneath the radical:
{{{ (8sqrt(2*3))/(2*3)(sqrt(2))}}}
{{{ (8sqrt(2*3))/6(sqrt(2))}}}
{{{ (4sqrt(2*3))/3sqrt(2)}}}
We can also break up the radical in the numerator thus:
{{{ (4sqrt(2)sqrt(3))/3sqrt(2)}}}
Canceling like-terms:
{{{ (4sqrt(3))/3}}}