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\frac{\frac{1}{12}}{\sqrt{\frac{1}{36}}}
Rewrite the square root of the division \frac{1}{144} as the division of square roots \frac{\sqrt{1}}{\sqrt{144}}. Take the square root of both numerator and denominator.
\frac{\frac{1}{12}}{\frac{1}{6}}
Rewrite the square root of the division \frac{1}{36} as the division of square roots \frac{\sqrt{1}}{\sqrt{36}}. Take the square root of both numerator and denominator.
\frac{1}{12}\times 6
Divide \frac{1}{12} by \frac{1}{6} by multiplying \frac{1}{12} by the reciprocal of \frac{1}{6}.
\frac{6}{12}
Multiply \frac{1}{12} and 6 to get \frac{6}{12}.
\frac{1}{2}
Reduce the fraction \frac{6}{12} to lowest terms by extracting and canceling out 6.