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\frac{\sqrt{11}}{\sqrt{111}}
Add 5 and 6 to get 11.
\frac{\sqrt{11}\sqrt{111}}{\left(\sqrt{111}\right)^{2}}
Rationalize the denominator of \frac{\sqrt{11}}{\sqrt{111}} by multiplying numerator and denominator by \sqrt{111}.
\frac{\sqrt{11}\sqrt{111}}{111}
The square of \sqrt{111} is 111.
\frac{\sqrt{1221}}{111}
To multiply \sqrt{11} and \sqrt{111}, multiply the numbers under the square root.