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\frac{\sqrt{55555666111}}{\sqrt{48822}}
Rewrite the square root of the division \sqrt{\frac{55555666111}{48822}} as the division of square roots \frac{\sqrt{55555666111}}{\sqrt{48822}}.
\frac{\sqrt{55555666111}\sqrt{48822}}{\left(\sqrt{48822}\right)^{2}}
Rationalize the denominator of \frac{\sqrt{55555666111}}{\sqrt{48822}} by multiplying numerator and denominator by \sqrt{48822}.
\frac{\sqrt{55555666111}\sqrt{48822}}{48822}
The square of \sqrt{48822} is 48822.
\frac{\sqrt{2712338730871242}}{48822}
To multiply \sqrt{55555666111} and \sqrt{48822}, multiply the numbers under the square root.