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\frac{55\sqrt{11}}{\left(\sqrt{11}\right)^{2}}
Rationalize the denominator of \frac{55}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.
\frac{55\sqrt{11}}{11}
The square of \sqrt{11} is 11.
5\sqrt{11}
Divide 55\sqrt{11} by 11 to get 5\sqrt{11}.