[tex]\frac{\sqrt{77}}{22}[/tex]
1) Consider this ratio. Since there is one radical in the denominator, we can rationalize it to simplify it:
[tex]\frac{\sqrt{7}}{2\sqrt{11}}=[/tex]
2) Let's multiply both numerator and denominator by its conjugate:
[tex]\frac{\sqrt{7}}{2\sqrt{11}}=\frac{\sqrt{7}\cdot\sqrt{11}}{2\sqrt{11}\cdot\sqrt{11}}=\frac{\sqrt{77}}{2\sqrt{11^2}}=\frac{\sqrt{77}}{22}[/tex]
Note that we rationalize it to simplify calculations. And we do that by getting rid of any radical on the bottom number as much as we can.
