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\frac{\frac{1}{11}\sqrt{x}}{\frac{1}{11}}=\frac{1}{\frac{1}{11}}
Multiply both sides by 11.
\sqrt{x}=\frac{1}{\frac{1}{11}}
Dividing by \frac{1}{11} undoes the multiplication by \frac{1}{11}.
\sqrt{x}=11
Divide 1 by \frac{1}{11} by multiplying 1 by the reciprocal of \frac{1}{11}.
x=121
Square both sides of the equation.