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\frac{\sqrt[2]{5}\sqrt{x}}{\sqrt[2]{5}}=\frac{\sqrt{55}}{\sqrt[2]{5}}
Divide both sides by \sqrt[2]{5}.
\sqrt{x}=\frac{\sqrt{55}}{\sqrt[2]{5}}
Dividing by \sqrt[2]{5} undoes the multiplication by \sqrt[2]{5}.
\sqrt{x}=\sqrt{11}
Divide \sqrt{55} by \sqrt[2]{5}.
x=11
Square both sides of the equation.